Bayesian models for longitudinal data

Longitudinal data, where data are repeatedly observed or measured on a temporal basis of time or age provides the foundation of the analysis of processes which evolve over time, and these can be referred to as growth or trajectory models. One of the traditional ways of looking at growth models is to employ either linear or polynomial functional forms to model trajectory shape, and account for variation around an overall mean trend with the inclusion of random eects or individual variation on the functional shape parameters. The identification of distinct subgroups or sub-classes (latent classes) within these trajectory models which are not based on some pre-existing individual classification provides an important methodology with substantive implications. The identification of subgroups or classes has a wide application in the medical arena where responder/non-responder identification based on distinctly diering trajectories delivers further information for clinical processes. This thesis develops Bayesian statistical models and techniques for the identification of subgroups in the analysis of longitudinal data where the number of time intervals is limited. These models are then applied to a single case study which investigates the neuropsychological cognition for early stage breast cancer patients undergoing adjuvant chemotherapy treatment from the Cognition in Breast Cancer Study undertaken by the Wesley Research Institute of Brisbane, Queensland. Alternative formulations to the linear or polynomial approach are taken which use piecewise linear models with a single turning point, change-point or knot at a known time point and latent basis models for the non-linear trajectories found for the verbal memory domain of cognitive function before and after chemotherapy treatment. Hierarchical Bayesian random eects models are used as a starting point for the latent class modelling process and are extended with the incorporation of covariates in the trajectory profiles and as predictors of class membership. The Bayesian latent basis models enable the degree of recovery post-chemotherapy to be estimated for short and long-term followup occasions, and the distinct class trajectories assist in the identification of breast cancer patients who maybe at risk of long-term verbal memory impairment.

Modelling and execution of asset management process via workflow automation

An Asset Management (AM) life-cycle constitutes a set of processes that align with the development, operation and maintenance of assets, in order to meet the desired requirements and objectives of the stake holders of the business. The scope of AM is often broad within an organization due to the interactions between its internal elements such as human resources, finance, technology, engineering operation, information technology and management, as well as external elements such as governance and environment. Due to the complexity of the AM processes, it has been proposed that in order to optimize asset management activities, process modelling initiatives should be adopted. Although organisations adopt AM principles and carry out AM initiatives, most do not document or model their AM processes, let alone enacting their processes (semi-) automatically using a computer-supported system. There is currently a lack of knowledge describing how to model AM processes through a methodical and suitable manner so that the processes are streamlines and optimized and are ready for deployment in a computerised way. This research aims to overcome this deficiency by developing an approach that will aid organisations in constructing AM process models quickly and systematically whilst using the most appropriate techniques, such as workflow technology. Currently, there is a wealth of information within the individual domains of AM and workflow. Both fields are gaining significant popularity in many industries thus fuelling the need for research in exploring the possible benefits of their cross-disciplinary applications. This research is thus inspired to investigate these two domains to exploit the application of workflow to modelling and execution of AM processes. Specifically, it will investigate appropriate methodologies in applying workflow techniques to AM frameworks. One of the benefits of applying workflow models to AM processes is to adapt and enable both ad-hoc and evolutionary changes over time. In addition, this can automate an AM process as well as to support the coordination and collaboration of people that are involved in carrying out the process. A workflow management system (WFMS) can be used to support the design and enactment (i.e. execution) of processes and cope with changes that occur to the process during the enactment. So far few literatures can be found in documenting a systematic approach to modelling the characteristics of AM processes. In order to obtain a workflow model for AM processes commonalities and differences between different AM processes need to be identified. This is the fundamental step in developing a conscientious workflow model for AM processes. Therefore, the first stage of this research focuses on identifying the characteristics of AM processes, especially AM decision making processes. The second stage is to review a number of contemporary workflow techniques and choose a suitable technique for application to AM decision making processes. The third stage is to develop an intermediate ameliorated AM decision process definition that improves the current process description and is ready for modelling using the workflow language selected in the previous stage. All these lead to the fourth stage where a workflow model for an AM decision making process is developed. The process model is then deployed (semi-) automatically in a state-of-the-art WFMS demonstrating the benefits of applying workflow technology to the domain of AM. Given that the information in the AM decision making process is captured at an abstract level within the scope of this work, the deployed process model can be used as an executable guideline for carrying out an AM decision process in practice. Moreover, it can be used as a vanilla system that, once being incorporated with rich information from a specific AM decision making process (e.g. in the case of a building construction or a power plant maintenance), is able to support the automation of such a process in a more elaborated way.

An investigation of a process for environmental banking appropriate to Queensland

This thesis examines the advanced North American environmental mitigation schemes for their applicability to Queensland. Compensatory wetland mitigation banking, in particular, is concerned with in-perpetuity management and protection - the basic concerns of the Queensland public about its unique environment. The process has actively engaged the North American market and become a thriving industry that (for the most part) effectively designs, creates and builds (or enhances) environmental habitat. A methodology was designed to undertake a comprehensive review of the history, evolution and concepts of the North American wetland mitigation banking system - before and after the implementation of a significant new compensatory wetland mitigation banking regulation in 2008. The Delphi technique was then used to determine the principles and working components of wetland mitigation banking. Results were then applied to formulate a questionnaire to review Australian marketbased instruments (including offsetting policies) against these North American principles. Following this, two case studies established guiding principles for implementation based on two components of the North American wetland mitigation banking program. The subsequent outcomes confirmed that environmental banking is a workable concept in North America and that it is worth applying in Queensland. The majority of offsetting policies in Australia have adopted some principles of the North American mitigation programs. Examination reveals that however, they fail to provide adequate incentives for private landowners to participate because the essential trading mechanisms are not employed. Much can thus be learnt from the North American situation - where private enterprise has devised appropriate free market concepts. The consequent environmental banking process (as adapted from the North American programs) should be implemented in Queensland. It can then focus here on engaging the private sector, where the majority of naturally productive lands are managed.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

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.

Developing a hybrid expert system program to aid in the design of plastic injection molding process

Experts in injection molding often refer to previous solutions to find a mold design similar to the current mold and use previous successful molding process parameters with intuitive adjustment and modification as a start for the new molding application. This approach saves a substantial amount of time and cost in experimental based corrective actions which are required in order to reach optimum molding conditions. A Case-Based Reasoning (CBR) System can perform the same task by retrieving a similar case which is applied to the new case from the case library and uses the modification rules to adapt a solution to the new case. Therefore, a CBR System can simulate human e~pertise in injection molding process design. This research is aimed at developing an interactive Hybrid Expert System to reduce expert dependency needed on the production floor. The Hybrid Expert System (HES) is comprised of CBR, flow analysis, post-processor and trouble shooting systems. The HES can provide the first set of operating parameters in order to achieve moldability condition and producing moldings free of stress cracks and warpage. In this work C++ programming language is used to implement the expert system. The Case-Based Reasoning sub-system is constructed to derive the optimum magnitude of process parameters in the cavity. Toward this end the Flow Analysis sub-system is employed to calculate the pressure drop and temperature difference in the feed system to determine the required magnitude of parameters at the nozzle. The Post-Processor is implemented to convert the molding parameters to machine setting parameters. The parameters designed by HES are implemented using the injection molding machine. In the presence of any molding defect, a trouble shooting subsystem can determine which combination of process parameters must be changed iii during the process to deal with possible variations. Constraints in relation to the application of this HES are as follows. - flow length (L) constraint: 40 mm < L < I 00 mm, - flow thickness (Th) constraint: -flow type: - material types: I mm < Th < 4 mm, unidirectional flow, High Impact Polystyrene (HIPS) and Acrylic. In order to test the HES, experiments were conducted and satisfactory results were obtained.

Coding speech signals at very low rates (below 1 kb/s) with high intelligibility

This thesis presents an original approach to parametric speech coding at rates below 1 kbitsjsec, primarily for speech storage applications. Essential processes considered in this research encompass efficient characterization of evolutionary configuration of vocal tract to follow phonemic features with high fidelity, representation of speech excitation using minimal parameters with minor degradation in naturalness of synthesized speech, and finally, quantization of resulting parameters at the nominated rates. For encoding speech spectral features, a new method relying on Temporal Decomposition (TD) is developed which efficiently compresses spectral information through interpolation between most steady points over time trajectories of spectral parameters using a new basis function. The compression ratio provided by the method is independent of the updating rate of the feature vectors, hence allows high resolution in tracking significant temporal variations of speech formants with no effect on the spectral data rate. Accordingly, regardless of the quantization technique employed, the method yields a high compression ratio without sacrificing speech intelligibility. Several new techniques for improving performance of the interpolation of spectral parameters through phonetically-based analysis are proposed and implemented in this research, comprising event approximated TD, near-optimal shaping event approximating functions, efficient speech parametrization for TD on the basis of an extensive investigation originally reported in this thesis, and a hierarchical error minimization algorithm for decomposition of feature parameters which significantly reduces the complexity of the interpolation process. Speech excitation in this work is characterized based on a novel Multi-Band Excitation paradigm which accurately determines the harmonic structure in the LPC (linear predictive coding) residual spectra, within individual bands, using the concept 11 of Instantaneous Frequency (IF) estimation in frequency domain. The model yields aneffective two-band approximation to excitation and computes pitch and voicing with high accuracy as well. New methods for interpolative coding of pitch and gain contours are also developed in this thesis. For pitch, relying on the correlation between phonetic evolution and pitch variations during voiced speech segments, TD is employed to interpolate the pitch contour between critical points introduced by event centroids. This compresses pitch contour in the ratio of about 1/10 with negligible error. To approximate gain contour, a set of uniformly-distributed Gaussian event-like functions is used which reduces the amount of gain information to about 1/6 with acceptable accuracy. The thesis also addresses a new quantization method applied to spectral features on the basis of statistical properties and spectral sensitivity of spectral parameters extracted from TD-based analysis. The experimental results show that good quality speech, comparable to that of conventional coders at rates over 2 kbits/sec, can be achieved at rates 650-990 bits/sec.

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.