Towards Bayesian experimental design for nonlinear models that require a large number of sampling times

The use of Bayesian methodologies for solving optimal experimental design problems has increased. Many of these methods have been found to be computationally intensive for design problems that require a large number of design points. A simulation-based approach that can be used to solve optimal design problems in which one is interested in finding a large number of (near) optimal design points for a small number of design variables is presented. The approach involves the use of lower dimensional parameterisations that consist of a few design variables, which generate multiple design points. Using this approach, one simply has to search over a few design variables, rather than searching over a large number of optimal design points, thus providing substantial computational savings. The methodologies are demonstrated on four applications, including the selection of sampling times for pharmacokinetic and heat transfer studies, and involve nonlinear models. Several Bayesian design criteria are also compared and contrasted, as well as several different lower dimensional parameterisation schemes for generating the many design points.

Fiber Bragg grating strain modulation based on nonlinear string transverse force amplifier

The only effective method of Fiber Bragg Grating (FBG) strain modulation has been by changing the distance between its two fixed ends. We demonstrate an alternative being more sensitive to force based on the nonlinear amplification relationship between a transverse force applied to a stretched string and its induced axial force. It may improve the sensitivity and size of an FBG force sensor, reduce the number of FBGs needed for multi-axial force monitoring, and control the resonant frequency of an FBG accelerometer.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

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.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Nonlinear actuator fault detection for small-scale UAS

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating corresponding velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.

A nonlinear position controller for maritime operations of Rotary-wing UAVs

This paper presents a disturbance attenuation controller for horizontal position stabilization for hover and automatic landings of a Rotary-wing Unmanned Aerial Vehicle (RUAV) operating in rough seas. Based on a helicopter model representing aerodynamics during the landing phase, a nonlinear state feedback H-infinity controller is designed to achieve rapid horizontal position tracking in a gusty environment. The resultant control variables are further treated in consideration of practical constraints (flapping dynamics, servo dynamics and time lag effect) for implementation purpose. The high-fidelity closed-loop simulation using parameters of the Vario helicopter verifies performance of the proposed position controller. It not only increases the disturbance attenuation capability of the RUAV, but also enables rapid position response when gusts occur. Comparative studies show that the H-infinity controller exhibits great performance improvement and can be applied to ship/RUAV landing systems.

Exploring new and emerging models for nonlinear performative works

This dissertation seeks to define and classify potential forms of Nonlinear structure and explore the possibilities they afford for the creation of new musical works. It provides the first comprehensive framework for the discussion of Nonlinear structure in musical works and provides a detailed overview of the rise of nonlinearity in music during the 20th century. Nonlinear events are shown to emerge through significant parametrical discontinuity at the boundaries between regions of relatively strong internal cohesion. The dissertation situates Nonlinear structures in relation to linear structures and unstructured sonic phenomena and provides a means of evaluating Nonlinearity in a musical structure through the consideration of the degree to which the structure is integrated, contingent, compressible and determinate as a whole. It is proposed that Nonlinearity can be classified as a three dimensional space described by three continuums: the temporal continuum, encompassing sequential and multilinear forms of organization, the narrative continuum encompassing processual, game structure and developmental narrative forms and the referential continuum encompassing stylistic allusion, adaptation and quotation. The use of spectrograms of recorded musical works is proposed as a means of evaluating Nonlinearity in a musical work through the visual representation of parametrical divergence in pitch, duration, timbre and dynamic over time. Spectral and structural analysis of repertoire works is undertaken as part of an exploration of musical nonlinearity and the compositional and performative features that characterize it. The contribution of cultural, ideological, scientific and technological shifts to the emergence of Nonlinearity in music is discussed and a range of compositional factors that contributed to the emergence of musical Nonlinearity is examined. The evolution of notational innovations from the mobile score to the screen score is plotted and a novel framework for the discussion of these forms of musical transmission is proposed. A computer coordinated performative model is discussed, in which a computer synchronises screening of notational information, provides temporal coordination of the performers through click-tracks or similar methods and synchronises the audio processing and synthesized elements of the work. It is proposed that such a model constitutes a highly effective means of realizing complex Nonlinear structures. A creative folio comprising 29 original works that explore nonlinearity is presented, discussed and categorised utilising the proposed classifications. Spectrograms of these works are employed where appropriate to illustrate the instantiation of parametrically divergent substructures and examples of structural openness through multiple versioning.

Locally weighted learning model predictive control for nonlinear and time varying dynamics

This paper proposes an online learning control system that uses the strategy of Model Predictive Control (MPC) in a model based locally weighted learning framework. The new approach, named Locally Weighted Learning Model Predictive Control (LWL-MPC), is proposed as a solution to learn to control robotic systems with nonlinear and time varying dynamics. This paper demonstrates the capability of LWL-MPC to perform online learning while controlling the joint trajectories of a low cost, three degree of freedom elastic joint robot. The learning performance is investigated in both an initial learning phase, and when the system dynamics change due to a heavy object added to the tool point. The experiment on the real elastic joint robot is presented and LWL-MPC is shown to successfully learn to control the system with and without the object. The results highlight the capability of the learning control system to accommodate the lack of mechanical consistency and linearity in a low cost robot arm.

Nonlinear pre-fire and post-fire analysis of steel frames

A numerical procedure based on the plastic hinge concept for study of the structural behaviour of steel framed structures exposed to fire is described. Most previous research on fire analysis considered the structural performance due to rising temperature. When strain reversal occurs during the cooling phase, the stress–strain curve is different. The plastic deformation is incorporated into the stress–strain curve to model the strain reversal effect in which unloading under elastic behaviour is allowed. This unloading response is traced by the incremental–iterative Newton–Raphson method. The mechanical properties of the steel member in the present fire analysis follows both Eurocode 3 Part 1.2 and BS5950 Part 8, which implicitly allow for thermal creep deformation. This paper presents an efficient fire analysis procedure for predicting thermal and cooling effects on an isolated element and a multi-storey frame. Several numerical and experimental examples related to structural behaviour in cooling phase are studied and compared with results obtained by other researchers. The proposed method is effective in the fire safety design and analysis of a building in a real fire scenario. The scope of investigation is of great significance since a large number of rescuers would normally enter a fire site as soon as the fire is extinguished and during the cooling phase, so a structural collapse can be catastrophic.

Model-predictive control and closed-loop stability considerations for nonlinear plants described by local ARX-type models

In this paper, a model-predictive control (MPC) method is detailed for the control of nonlinear systems with stability considerations. It will be assumed that the plant is described by a local input/output ARX-type model, with the control potentially included in the premise variables, which enables the control of systems that are nonlinear in both the state and control input. Additionally, for the case of set point regulation, a suboptimal controller is derived which has the dual purpose of ensuring stability and enabling finite-iteration termination of the iterative procedure used to solve the nonlinear optimization problem that is used to determine the control signal.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.