An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Advanced analysis of steel frame structures comprising non-compact sections

During the past decade, a significant amount of research has been conducted internationally with the aim of developing, implementing, and verifying "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures. Application of these methods permits comprehensive assessment of the actual failure modes and ultimate strengths of structural systems in practical design situations, without resort to simplified elastic methods of analysis and semi-empirical specification equations. Advanced analysis has the potential to extend the creativity of structural engineers and simplify the design process, while ensuring greater economy and more uniform safety with respect to the ultimate limit state. The application of advanced analysis methods has previously been restricted to steel frames comprising only members with compact cross-sections that are not subject to the effects of local buckling. This precluded the use of advanced analysis from the design of steel frames comprising a significant proportion of the most commonly used Australian sections, which are non-compact and subject to the effects of local buckling. This thesis contains a detailed description of research conducted over the past three years in an attempt to extend the scope of advanced analysis by developing methods that include the effects of local buckling in a non-linear analysis formulation, suitable for practical design of steel frames comprising non-compact sections. Two alternative concentrated plasticity formulations are presented in this thesis: the refined plastic hinge method and the pseudo plastic zone method. Both methods implicitly account for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the methods for the analysis of steel frames comprising non-compact sections has been established by comparison with a comprehensive range of analytical benchmark frame solutions. Both the refined plastic hinge and pseudo plastic zone methods are more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations. For example, the pseudo plastic zone method predicts the ultimate strength of the analytical benchmark frames with an average conservative error of less than one percent, and has an acceptable maximum unconservati_ve error of less than five percent. The pseudo plastic zone model can allow the design capacity to be increased by up to 30 percent for simple frames, mainly due to the consideration of inelastic redistribution. The benefits may be even more significant for complex frames with significant redundancy, which provides greater scope for inelastic redistribution. The analytical benchmark frame solutions were obtained using a distributed plasticity shell finite element model. A detailed description of this model and the results of all the 120 benchmark analyses are provided. The model explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. Its accuracy was verified by comparison with a variety of analytical solutions and the results of three large-scale experimental tests of steel frames comprising non-compact sections. A description of the experimental method and test results is also provided.

An optimization-based algorithm for shunt active filter under distorted supply voltages

When the supply voltages are balanced and sinusoidal, load compensation can give both unity power factor (UPF) and perfect harmonic cancellation (PHC) source currents. But under distorted supply voltages, achieving both UPF and PHC currents are not possible and contradictory to each other. Hence there should be an optimal performance between these two important compensation goals. This paper presents an optimal control algorithm for load compensation under unbalanced and distorted supply voltages. In this algorithm source currents are compensated for reactive, imbalance components and harmonic distortions set by the limits. By satisfying the harmonic distortion limits and power balance, this algorithm gives the source currents which will provide the maximum achievable power factor. The detailed simulation results using MATLAB are presented to support the performance of the proposed optimal control algorithm.

Multi-linear strategies for (re)presenting the complexity of young people in research

Within the current climate of unpredictability and constant change, young people at school are faced with a multitude of choices and contradictory influences. In this article, I argue that (re)presentations of young people in youth research need to reflect the complexity and multiplicity of their lives and changing priorities, and I attempt to (re)present a small group of young people in this particular milieu. I illustrate some of the competing influences in their lives, and I outline some specific strategies that are useful for (re)presenting these contextual worlds. The strategies I advocate disrupt the homogenous representations of ‘youth’ as a developmental phase and instead reflect the diverse spheres of influence which shape their subjectivities and practices.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, commonly employ Bank-to-Turn ma- neuvers to change heading and thus direction of travel. Whilst effective, banking an aircraft during the inspection of ground based features hinders data collection, with body fixed sen- sors angled away from the direction of turn and a panning motion induced through roll rate that can reduce data quality. By adopting Skid-to-Turn maneuvers, the aircraft can change heading whilst maintaining wings level flight, thus allowing body fixed sensors to main- tain a downward facing orientation. An Image-Based Visual Servo controller is developed to directly control the position of features as captured by onboard inspection sensors. This improves on the indirect approach taken by other tracking controllers where a course over ground directly above the feature is assumed to capture it centered in the field of view. Performance of the proposed controller is compared against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to replicate the field of view of a body fixed camera.

Optimization of long rural feeders using a genetic algorithm

This paper describes the optimization of conductor size and the voltage regulator location & magnitude of long rural distribution lines. The optimization minimizes the lifetime cost of the lines, including capital costs and losses while observing voltage drop and operational constraints using a Genetic Algorithm (GA). The GA optimization is applied to a real Single Wire Earth Return (SWER) network in regional Queensland and results are presented.

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

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

Parallel linear system solution and its application to railway power network simulation

The Streaming SIMD extension (SSE) is a special feature embedded in the Intel Pentium III and IV classes of microprocessors. It enables the execution of SIMD type operations to exploit data parallelism. This article presents improving computation performance of a railway network simulator by means of SSE. Voltage and current at various points of the supply system to an electrified railway line are crucial for design, daily operation and planning. With computer simulation, their time-variations can be attained by solving a matrix equation, whose size mainly depends upon the number of trains present in the system. A large coefficient matrix, as a result of congested railway line, inevitably leads to heavier computational demand and hence jeopardizes the simulation speed. With the special architectural features of the latest processors on PC platforms, significant speed-up in computations can be achieved.

A parallel solution to linear systems

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III and IV classes of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving linear systems with SSE and discuss advantages and disadvantages of this approach based on our experimental study.

Performance optimization for parallel processing on a multiple-CPU server

Symmetric multi-processor (SMP) systems, or multiple-CPU servers, are suitable for implementing parallel algorithms because they employ dedicated communication devices to enhance the inter-processor communication bandwidth, so that a better performance can be obtained. However, the cost for a multiple-CPU server is high and therefore, the server is usually shared among many users. The work-load due to other users will certainly affect the performance of the parallel programs so it is desirable to derive a method to optimize parallel programs under different loading conditions. In this paper, we present a simple method, which can be applied in SPMD type parallel programs, to improve the speedup by controlling the number of threads within the programs.