Many hours are spent by systemand control engineers deriving reduced order dynamicmodels portraying the dominant systemdynamics of thermohydraulic systems. A need therefore exists to develop a method that will automate the model derivation process. The model format preferred for control system design and analysis during preliminary system design is the state space format. The aim of this study is therefore to develop an automated and generic state space model extraction method that can be applied to thermohydraulic systems. Well developed system identification methods exist for obtaining state space models from input-output data, but these models are not transparent, meaning the parameters do not have any physical meaning. For example one cannot identify system parameters such as heat or mass transfer coefficients. Another approach is needed to derive state space models automatically. Many commercial thermohydraulic simulation codes follow a network approach towards the representation of thermohydraulic systems. This approach is probably one of the most advanced approaches in terms of technical development. It would therefore be useful to develop a state space extraction algorithm that would be able to derive reduced order state space models from network representations of thermohydraulic systems. In this regard a network approach is followed in the development of the state space extraction algorithm. The advantage of using a network-based extraction method is that the extracted state space model is transparent and the algorithm can be embedded in existing simulation software that follow a network approach. In this study an existing state space extraction algorithm, used for electrical network analysis, is modified and applied in a new way to extract state space models of thermohydraulic systems. A thermohydraulic system is partitioned into its respective physical domains which, unlike electrical systems, have multiple variables. Network representations are derived for each domain. The state space algorithm is applied to these network representations to extract symbolic state spacemodels. The symbolic parametersmay then be substitutedwith numerical values. The state space extraction algorithm is applied to small scale thermohydraulic systems such as a U-tube and a heat exchanger, but also to a larger, more complex system such as the Pebble Bed Modular Reactor Power Conversion Unit (PBMR PCU). It is also shown that the algorithm can extract linear, nonlinear, time-varying and time-invariant state space models. The extracted state space models are validated by solving the state space models and comparing the solutions with Flownex results. Flownex is an advanced and extensively validated thermo-fluid simulation code. The state space models compared well with Flownex results. The usefulness of the state space model extraction algorithm in model-based control system design is illustrated by extracting a linear time-invariant state space model of the PBMR PCU. This model is embedded in an optimal model-based control scheme called Model-Predictive Control (MPC). The controller is compared with standard optimised control schemes such as PID and Fuzzy PID control. The MPC controller shows superior performance compared to these control schemes. This study succeeded in developing an automated state space model extraction method that can be applied to thermohydraulic networks. Hours spent on writing down equations from first principles to derive reduced order models for control purposes can now be replaced with a click of a button. The need for an automated state space model extraction method for thermohydraulic systems has therefore been resolved / Thesis (Ph.D. (Computer and Electronical Engineering)--North-West University, Potchefstroom Campus, 2009.

Many hours are spent by systemand control engineers deriving reduced order dynamicmodels portraying the dominant systemdynamics of thermohydraulic systems. A need therefore exists to develop a method that will automate the model derivation process. The model format preferred for control system design and analysis during preliminary system design is the state space format. The aim of this study is therefore to develop an automated and generic state space model extraction method that can be applied to thermohydraulic systems. Well developed system identification methods exist for obtaining state space models from input-output data, but these models are not transparent, meaning the parameters do not have any physical meaning. For example one cannot identify system parameters such as heat or mass transfer coefficients. Another approach is needed to derive state space models automatically. Many commercial thermohydraulic simulation codes follow a network approach towards the representation of thermohydraulic systems. This approach is probably one of the most advanced approaches in terms of technical development. It would therefore be useful to develop a state space extraction algorithm that would be able to derive reduced order state space models from network representations of thermohydraulic systems. In this regard a network approach is followed in the development of the state space extraction algorithm. The advantage of using a network-based extraction method is that the extracted state space model is transparent and the algorithm can be embedded in existing simulation software that follow a network approach. In this study an existing state space extraction algorithm, used for electrical network analysis, is modified and applied in a new way to extract state space models of thermohydraulic systems. A thermohydraulic system is partitioned into its respective physical domains which, unlike electrical systems, have multiple variables. Network representations are derived for each domain. The state space algorithm is applied to these network representations to extract symbolic state spacemodels. The symbolic parametersmay then be substitutedwith numerical values. The state space extraction algorithm is applied to small scale thermohydraulic systems such as a U-tube and a heat exchanger, but also to a larger, more complex system such as the Pebble Bed Modular Reactor Power Conversion Unit (PBMR PCU). It is also shown that the algorithm can extract linear, nonlinear, time-varying and time-invariant state space models. The extracted state space models are validated by solving the state space models and comparing the solutions with Flownex results. Flownex is an advanced and extensively validated thermo-fluid simulation code. The state space models compared well with Flownex results. The usefulness of the state space model extraction algorithm in model-based control system design is illustrated by extracting a linear time-invariant state space model of the PBMR PCU. This model is embedded in an optimal model-based control scheme called Model-Predictive Control (MPC). The controller is compared with standard optimised control schemes such as PID and Fuzzy PID control. The MPC controller shows superior performance compared to these control schemes. This study succeeded in developing an automated state space model extraction method that can be applied to thermohydraulic networks. Hours spent on writing down equations from first principles to derive reduced order models for control purposes can now be replaced with a click of a button. The need for an automated state space model extraction method for thermohydraulic systems has therefore been resolved / Thesis (Ph.D. (Computer and Electronical Engineering)--North-West University, Potchefstroom Campus, 2009.

Probabilistic models are dominant in many research areas. To learn those models we need to find a way to determine parameters of distributions over variables which are included in the model. The main focus of my research is related to continuous variables. Thus, Gaussian distribution over variables is the most dominant factor in all models used in this document. I have been working on different and important real-life problems such as Uncertainty of Neural Network Based Aerosol Retrieval, Regression Learning with Multiple Noise Oracles and Model Predictive Control (MPC) for Sepsis Treatment, Clustering Causes of Action in Federal Courts. These problems will be discussed in the following chapters. Aerosols, small particles emanating from natural and man-made sources, along with green house gases have been recognized as very important factors in ongoing climate changes. Accurate estimation of aerosol composition and concentration is one of the main challenges in current climate research. Algorithm for prediction of aerosol designed by domain scientists does not provide quantitative information about aerosol estimation uncertainty. We deployed algorithm which uses neural networks to determine both uncertainty and the estimation of the aerosol. The uncertainty estimator has been built under an assumption that uncertainty is a function of variables used for aerosol prediction. Also, the uncertainty of predictions has been computed as the variance of the conditional distribution of targets given the input data. In regression learning, it is often difficult to obtain the true values of the label variables, while multiple sources of noisy estimates of lower quality are readily available. To address this problem, I propose a new Bayesian approach that learns a regression model from a data with noisy labels which are provided by multiple oracles. This method gives closed form solution for model parameters and it is applicable to both linear and nonlinear regression problems. Sepsis is a medical condition characterized as a systemic inflammatory response to an infection. High mortality rate (30-35%) of septic patients is usually caused by inadequate treatment. Thus, development of tools that can aid clinicians in designing optimal strategies for inflammation treatments is of utmost importance. Towards this objective I developed a data driven approach for therapy optimization where a predictive model for patients' behavior is learned directly from historical data. As such, the predictive model is incorporated into a model predictive control optimization algorithm to find optimal therapy, which will lead the patient to a healthy state. A more careful targeting of specific therapeutic strategies to more biologically homogeneous groups of patients is essential to developing effective sepsis treatment. We propose a kernel-based approach to characterize dynamics of inflammatory response in a heterogeneous population of septic patients. The method utilizes Linear State Space Control (LSSC) models to take into account dynamics of inflammatory response over time as well as the effect of therapy applied to the patient. We use a similarity measure defined on kernels of LSSC models to find homogeneous groups of patients. In addition to clustering of dynamics of inflammatory response we also explored a clustering of civil litigation from its inception by examining the content of civil complaints. We utilize spectral cluster analysis on a newly compiled federal district court dataset of causes of action in complaints to illustrate the relationship of legal claims to one another, the broader composition of lawsuits in trial courts, and the breadth of pleading in individual complaints. Our results shed light not only on the networks of legal theories in civil litigation but also on how lawsuits are classified and the strategies that plaintiffs and their attorneys employ when commencing litigation. / Computer and Information Science

A common interest of scientists in many fields is to understand the relationship between the dynamics of a physical system and the occurrences of discrete events within such physical system. Seismologists study the connection between mechanical vibrations of the Earth and the occurrences of earthquakes so that future earthquakes can be better predicted. Astrophysicists study the association between the oscillating energy of celestial regions and the emission of photons to learn the Universe's various objects and their interactions. Neuroscientists study the link between behavior and the millisecond-timescale spike patterns of neurons to understand higher brain functions. Such relationships can often be formulated within the framework of state-space models with point process observations. The basic idea is that the dynamics of the physical systems are driven by the dynamics of some stochastic state variables and the discrete events we observe in an interval are noisy observations with distributions determined by the state variables. This thesis proposes several new methodological developments that advance the framework of state-space models with point process observations at the intersection of statistics and neuroscience. In particular, we develop new methods 1) to characterize the rhythmic spiking activity using history-dependent structure, 2) to model population spike activity using marked point process models, 3) to allow for real-time decision making, and 4) to take into account the need for dimensionality reduction for high-dimensional state and observation processes. We applied these methods to a novel problem of tracking rhythmic dynamics in the spiking of neurons in the subthalamic nucleus of Parkinson's patients with the goal of optimizing placement of deep brain stimulation electrodes. We developed a decoding algorithm that can make decision in real-time (for example, to stimulate the neurons or not) based on various sources of information present in population spiking data. Lastly, we proposed a general three-step paradigm that allows us to relate behavioral outcomes of various tasks to simultaneously recorded neural activity across multiple brain areas, which is a step towards closed-loop therapies for psychological diseases using real-time neural stimulation. These methods are suitable for real-time implementation for content-based feedback experiments.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion.

In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if the likelihood is continuous in the parameters, the estimates produced by practical particle filters are not, even when common random numbers are used for each filter. This is because the same resampling step which drastically reduces the variance of the estimates also introduces discontinuities in the particles that are selected across filters when the parameters change. When the state variables are univariate, a method exists that gives an estimator of the log-likelihood that is continuous in the parameters. We present a non-trivial generalization of this method using tree-based o(N²) (and as low as O(N log N)) resampling schemes that induce significant correlation amongst the selected particles across filters. In turn, this reduces the variance of the difference between the likelihood evaluated for different values of the parameters and the resulting estimator is considerably smoother than naively running the filters with common random numbers. Importantly, in practice our methods require only a change to the resample operation in the SMC framework without the addition of any extra parameters and can therefore be used for any application in which particle filters are already used. In addition, excepting the optional use of interpolation in the schemes, there are no regularity conditions for their use although certain conditions make them more advantageous. In this thesis, we first introduce the relevant aspects of the SMC methodology to the task of likelihood estimation in continuous state-space models and present an overview of work related to the task of smooth likelihood estimation. Following this, we introduce theoretically correct resampling schemes that cannot be implemented and the practical tree-based resampling schemes that were developed instead. After presenting the performance of our schemes in various applications, we show that two of the schemes are asymptotically consistent with the theoretically correct but unimplementable methods introduced earlier. Finally, we conclude the thesis with a discussion. / Science, Faculty of / Computer Science, Department of / Graduate

Glaucoma is a degenerative disease that damages the nerve fiber layer in the retina of the eye. Its mechanisms are not fully known and there is no fully-effective strategy to prevent visual impairment and blindness. However, if treatment is carried out at an early stage, it is possible to slow glaucomatous progression and improve the quality of life of sufferers. Despite the great amount of heterogeneous data that has become available for monitoring glaucoma, the performance of tests for early diagnosis are still insufficient, due to the complexity of disease progression and the diffculties in obtaining sufficient measurements. This research aims to assess and extend Bayesian Network (BN) models to investigate the nature of the disease and its progression, as well as improve early diagnosis performance. The exibility of BNs and their ability to integrate with clinician expertise make them a suitable tool to effectively exploit the available data. After presenting the problem, a series of BN models for cross-sectional data classification and integration are assessed; novel techniques are then proposed for classification and modelling of glaucoma progression. The results are validated against literature, direct expert knowledge and other Artificial Intelligence techniques, indicating that BNs and their proposed extensions improve glaucoma diagnosis performance and enable new insights into the disease process.

This thesis presents an empirical analysis of the unemployment hysteresis in the Czech Republic on quarterly data from 1999 to 2015. The hysteresis is modelled by allowing for: (i) impact of the cyclical unemployment on the NAIRU; (ii) impact of the long-term un- employment on the NAIRU. Models are written in state space form and estimated using Bayesian approach. The main contributions of this thesis are as follows. The results pro- vide robust evidence in favour of the hysteresis in the Czech Republic, but precise size of the hysteresis effect is surrounded by relatively large uncertainty. Posterior mean estimates of key parameters indicate that in response to increase in the cyclical unemployment of 1 percentage point, the NAIRU increases by 0.15 percentage points. The first specification of the hysteresis implies that the hysteresis induced changes in the Czech Republic's NAIRU of at most 1 percentage point. The hysteresis specified as impact of the long-term unemploy- ment on the NAIRU then implies even weaker effect, inducing changes in the NAIRU of at most 0.6 percentage points. The models are estimated jointly with the hybrid Phillips curve identified using survey forecasts as proxies for the expectations. Estimate of the expecta- tions' parameter 0.65 indicates the forward-looking nature of the Czech...

<p>Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.</p> / Dissertation