Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Development of real-time process control systems using formal techniques

A major application of computers has been to control physical processes in which the computer is embedded within some large physical process and is required to control concurrent physical processes. The main difficulty with these systems is their event-driven characteristics, which complicate their modelling and analysis. Although a number of researchers in the process system community have approached the problems of modelling and analysis of such systems, there is still a lack of standardised software development formalisms for the system (controller) development, particular at early stage of the system design cycle. This research forms part of a larger research programme which is concerned with the development of real-time process-control systems in which software is used to control concurrent physical processes. The general objective of the research in this thesis is to investigate the use of formal techniques in the analysis of such systems at their early stages of development, with a particular bias towards an application to high speed machinery. Specifically, the research aims to generate a standardised software development formalism for real-time process-control systems, particularly for software controller synthesis. In this research, a graphical modelling formalism called Sequential Function Chart (SFC), a variant of Grafcet, is examined. SFC, which is defined in the international standard IEC1131 as a graphical description language, has been used widely in industry and has achieved an acceptable level of maturity and acceptance. A comparative study between SFC and Petri nets is presented in this thesis. To overcome identified inaccuracies in the SFC, a formal definition of the firing rules for SFC is given. To provide a framework in which SFC models can be analysed formally, an extended time-related Petri net model for SFC is proposed and the transformation method is defined. The SFC notation lacks a systematic way of synthesising system models from the real world systems. Thus a standardised approach to the development of real-time process control systems is required such that the system (software) functional requirements can be identified, captured, analysed. A rule-based approach and a method called system behaviour driven method (SBDM) are proposed as a development formalism for real-time process-control systems.

Comparative performance of analytical techniques for polyhexamethylene biguanide (PHMB) in ophthalmic solutions

Purpose: The use of PHMB as a disinfectant in contact lens multipurpose solutions has been at the centre of much debate in recent times, particularly in relation to the issue of solution induced corneal staining. Clinical studies have been carried out which suggest different effects with individual contact lens materials used in combination with specific PHMB containing care regimes. There does not appear to be, however, a reliable analytical technique that would detect and quantify with any degree of accuracy the specific levels of PHMB that are taken up and released from individual solutions by the various contact lens materials. Methods: PHMB is a mixture of positively charged polymer units of varying molecular weight that has maximum absorbance wavelength of 236 nm. On the basis of these properties a range of assays including capillary electrophoresis, HPLC, a nickelnioxime colorimetric technique, mass spectrophotometry, UV spectroscopy and ion chromatography were assessed paying particular attention to each of their constraints and detection levels. Particular interest was focused on the relative advantage of contactless conductivity compared to UV and mass spectrometry detection in capillary electrophoresis (CE). This study provides an overview of the comparative performance of these techniques. Results: The UV absorbance of PHMB solutions, ranging from 0.0625 to 50 ppm was measured at 236 nm. Within this range the calibration curve appears to be linear however, absorption values below 1 ppm (0.0001%) were extremely difficult to reproduce. The concentration of PHMB in solutions is in the range of 0.0002–0.00005% and our investigations suggest that levels of PHMB below 0.0001% (levels encountered in uptake and release studies) can not be accurately estimated, in particular when analysing complex lens care solutions which can contain competitively absorbing, and thus interfering, species in the solution. The use of separative methodologies, such as CE using UV detection alone is similarly limited. Alternative techniques including contactless conductivity detection offer greater discrimination in complex solutions together with the opportunity for dual channel detection. Preliminary results achieved by TraceDec1 contactless conductivity detection, (Gain 150%, Offset 150) in conjunction with the Agilent capillary electrophoresis system using a bare fused silica capillary (extended light path, 50 mid, total length 64.5 cm, effective length 56 cm) and a cationic buffer at pH 3.2, exhibit great potential with reproducible PHMB split peaks. Conclusions: PHMB-based solutions are commonly associated with the potential to invoke corneal staining in combination with certain contact lens materials. However this terminology ‘PHMBbased solution’ is used primarily because PHMB itself has yet to be adequately implicated as the causative agent of the staining and compromised corneal cell integrity. The lack of well characterised adequately sensitive assays, coupled with the range of additional components that characterise individual care solutions pose a major barrier to the investigation of PHMB interactions in the lenswearing eye.

Extended reach of 116 Gb/s DP-QPSK transmission using random DFB fiber laser based Raman amplification and bidirectional second-order pumping

We propose a novel random DFB fiber laser based Raman amplification using bidirectional second-order pumping. This extends the reach of 116 Gb/s DP-QPSK WDM transmission up to 7915 km, compared with other Raman amplification techniques.