Kalman-filter-based EEG source localization

This thesis uses the Kalman filter (KF) to solve the electroencephalographic (EEG) inverse problem to image its neuronal sources. Chapter 1 introduces EEG source localization and the KF and discusses how it can solve the inverse problem. Chapter 2 introduces an EEG inverse solution using a spatially whitened KF (SWKF) to reduce the computational burden. Likelihood maximization is used to fit spatially uniform neural model parameters to simulated and clinical EEGs. The SWKF accurately reconstructs source dynamics. Filter performance is analyzed by computing the innovations’ statistical properties and identifying spatial variations in performance that could be improved by use of spatially varying parameters. Chapter 3 investigates the SWKF via one-dimensional (1D) simulations. Motivated by Chapter 2, two model parameters are given Gaussian spatial profiles to better reflect brain dynamics. Constrained optimization ensures estimated parameters have clear biophysical interpretations. Inverse solutions are also computed using the optimal linear KF. Both filters produce accurate state estimates. Spatially varying parameters are correctly identified from datasets with transient dynamics, but estimates for driven datasets are degraded by the unmodeled drive term. Chapter 4 treats the whole-brain EEG inverse problem and applies features of the 1D simulations to the SWKF of Chapter 2. Spatially varying parameters are used to model spatial variation of the alpha rhythm. The simulated EEG here exhibits wave-like patterns and spatially varying dynamics. As in Chapter 3, optimization constrains model parameters to appropriate ranges. State estimation is again reliable for simulated and clinical EEG, although spatially varying parameters do not improve accuracy and parameter estimation is unreliable, with wave velocity underestimated. Contributing factors are identified and approaches to overcome them are discussed. Chapter 5 summarizes the main findings and outlines future work

Kalman-filter-based EEG source localization

This thesis uses the Kalman filter (KF) to solve the electroencephalographic (EEG) inverse problem to image its neuronal sources. Chapter 1 introduces EEG source localization and the KF and discusses how it can solve the inverse problem. Chapter 2 introduces an EEG inverse solution using a spatially whitened KF (SWKF) to reduce the computational burden. Likelihood maximization is used to fit spatially uniform neural model parameters to simulated and clinical EEGs. The SWKF accurately reconstructs source dynamics. Filter performance is analyzed by computing the innovations’ statistical properties and identifying spatial variations in performance that could be improved by use of spatially varying parameters. Chapter 3 investigates the SWKF via one-dimensional (1D) simulations. Motivated by Chapter 2, two model parameters are given Gaussian spatial profiles to better reflect brain dynamics. Constrained optimization ensures estimated parameters have clear biophysical interpretations. Inverse solutions are also computed using the optimal linear KF. Both filters produce accurate state estimates. Spatially varying parameters are correctly identified from datasets with transient dynamics, but estimates for driven datasets are degraded by the unmodeled drive term. Chapter 4 treats the whole-brain EEG inverse problem and applies features of the 1D simulations to the SWKF of Chapter 2. Spatially varying parameters are used to model spatial variation of the alpha rhythm. The simulated EEG here exhibits wave-like patterns and spatially varying dynamics. As in Chapter 3, optimization constrains model parameters to appropriate ranges. State estimation is again reliable for simulated and clinical EEG, although spatially varying parameters do not improve accuracy and parameter estimation is unreliable, with wave velocity underestimated. Contributing factors are identified and approaches to overcome them are discussed. Chapter 5 summarizes the main findings and outlines future work

State estimators in soft sensing and sensor fusion for sustainable manufacturing

State estimators, including observers and Bayesian filters, are a class of model-based algorithms for estimating variables in a dynamical system given sensor measurements of related system states. They can be used to derive fast and accurate estimates of system variables which cannot be measured directly (’soft sensing’) or for which only noisy, intermittent, delayed, indirect or unreliable measurements are available, perhaps from multiple sources (’sensor fusion’). In this paper we introduce the concepts and main methods of state estimation and review recent applications in improving the sustainability of manufacturing processes. It is shown that state estimation algorithms can play a key role in manufacturing systems to accurately monitor and control processes to improve efficiencies, lower environmental impact, enhance product quality, improve the feasibility of processing more sustainable raw materials, and ensure safer working environments for humans. We discuss current and emerging trends in using state estimation as a framework for combining physical knowledge with other sources of data for monitoring and control of distributed manufacturing systems

Iterative learning control of crystallisation systems

Under the increasing pressure of issues like reducing the time to market, managing lower production costs, and improving the flexibility of operation, batch process industries thrive towards the production of high value added commodity, i.e. specialty chemicals, pharmaceuticals, agricultural, and biotechnology enabled products. For better design, consistent operation and improved control of batch chemical processes one cannot ignore the sensing and computational blessings provided by modern sensors, computers, algorithms, and software. In addition, there is a growing demand for modelling and control tools based on process operating data. This study is focused on developing process operation data-based iterative learning control (ILC) strategies for batch processes, more specifically for batch crystallisation systems. In order to proceed, the research took a step backward to explore the existing control strategies, fundamentals, mechanisms, and various process analytical technology (PAT) tools used in batch crystallisation control. From the basics of the background study, an operating data-driven ILC approach was developed to improve the product quality from batch-to-batch. The concept of ILC is to exploit the repetitive nature of batch processes to automate recipe updating using process knowledge obtained from previous runs. The methodology stated here was based on the linear time varying (LTV) perturbation model in an ILC framework to provide a convergent batch-to-batch improvement of the process performance indicator. In an attempt to create uniqueness in the research, a novel hierarchical ILC (HILC) scheme was proposed for the systematic design of the supersaturation control (SSC) of a seeded batch cooling crystalliser. This model free control approach is implemented in a hierarchical structure by assigning data-driven supersaturation controller on the upper level and a simple temperature controller in the lower level. In order to familiarise with other data based control of crystallisation processes, the study rehearsed the existing direct nucleation control (DNC) approach. However, this part was more committed to perform a detailed strategic investigation of different possible structures of DNC and to compare the results with that of a first principle model based optimisation for the very first time. The DNC results in fact outperformed the model based optimisation approach and established an ultimate guideline to select the preferable DNC structure. Batch chemical processes are distributed as well as nonlinear in nature which need to be operated over a wide range of operating conditions and often near the boundary of the admissible region. As the linear lumped model predictive controllers (MPCs) often subject to severe performance limitations, there is a growing demand of simple data driven nonlinear control strategy to control batch crystallisers that will consider the spatio-temporal aspects. In this study, an operating data-driven polynomial chaos expansion (PCE) based nonlinear surrogate modelling and optimisation strategy was presented for batch crystallisation processes. Model validation and optimisation results confirmed this approach as a promise to nonlinear control. The evaluations of the proposed data based methodologies were carried out by simulation case studies, laboratory experiments and industrial pilot plant experiments. For all the simulation case studies a detailed mathematical models covering reaction kinetics and heat mass balances were developed for a batch cooling crystallisation system of Paracetamol in water. Based on these models, rigorous simulation programs were developed in MATLAB®, which was then treated as the real batch cooling crystallisation system. The laboratory experimental works were carried out using a lab scale system of Paracetamol and iso-Propyl alcohol (IPA). All the experimental works including the qualitative and quantitative monitoring of the crystallisation experiments and products demonstrated an inclusive application of various in situ process analytical technology (PAT) tools, such as focused beam reflectance measurement (FBRM), UV/Vis spectroscopy and particle vision measurement (PVM) as well. The industrial pilot scale study was carried out in GlaxoSmithKline Bangladesh Limited, Bangladesh, and the system of experiments was Paracetamol and other powdered excipients used to make paracetamol tablets. The methodologies presented in this thesis provide a comprehensive framework for data-based dynamic optimisation and control of crystallisation processes. All the simulation and experimental evaluations of the proposed approaches emphasised the potential of the data-driven techniques to provide considerable advances in the current state-of-the-art in crystallisation control