Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Investigation ofsolid - state cooler based on electrocaloric effect

Electrocaloric cooling based on ability of material to change temperature by applying an electric field under adiabatic conditions is relatively new and challenging direction of ferroelectrics research. In this work we report about analytical, simulation and experimental data for BaSrTiO3 thin film and bulk ceramic samples. Detailed discussion of a theoretical base of the electrocaloric effect is included. Demonstrated experimental and computational results exemplify rational approach to a problem of solid-state cooler construction.

Chelyabinsk CHP-3 “locked power” problem solving

All over the world power systems become bigger and bigger every day. New equipment is installed, new feeders are constructed, new power units are installed. Some old elements of the network, however, are not changed in time. As a result, “bottlenecks” for capacity transmission can occur. By locked power problem the situation when a power plant has installed capacity exceeding the power it can actually deliver is usually meant. Regime, scheme or even technical restrictions-related issues usually cause this kind of problem. It is really important, since from the regime point of view it is typical decision to have a mobile capacity reserve, in case of malfunctions. And, what can be even more significant, power plant owner (JSC Fortum in our case) losses his money because of selling less electrical energy. The goal of master`s thesis is to analyze the current state of Chelyabinsk power system and the CHP-3 (Combined Heat and Power plant) in particular in relation with it`s ability to deliver the whole capacity of the CHP in it`s existing state and also taking into consideration the prospect of power unit 3 installation by the fourth quarter of 2010. The thesis contains some general information about the UPS of Russia, CPS of Ural, power system of Chelyabinsk and the Chelyabinsk region itself. Then the CHP-3 is described from technical point of view with it`s equipment observation. Regimes for the nowadays power system and for the system after the power unit 3 installation are reviewed. The problems occurring are described and, finally, a solution is offered.

Design and implementation of a production synchronization extension for Microsoft Dynamics AX

In a just-in-time, assemble-to-order production environments the scheduling of material requirements and production tasks - even though difficult - is of paramount importance. Different enterprise resource planning solutions with master scheduling functionality have been created to ease this problem and work as expected unless there is a problem in the material flow. This case-based candidate’s thesis introduces a tool for Microsoft Dynamics AX multisite environment, that can be used by site managers and production coordinators to get an overview of the current open sales order base and prioritize production in the event of material shortouts to avoid part-deliveries.

Waste Management in Commercial Activity: State-of-the-Art and the Potential Innovation in the Urban Areas of Hanoi, Vietnam

As the rapid development of the society as well as the lifestyle, the generation of commercial waste is getting more complicated to control. The situation of packaging waste and food waste – the main fractions of commercial waste in different countries in Europe and Asia is analyzed in order to evaluate and suggest necessary improvements for the existing waste management system in the city of Hanoi, Vietnam. From all waste generation sources of the city, a total amount of approximately 4000 tons of mixed waste is transported to the composting facility and the disposal site, which emits a huge amount of 1,6Mt of GHG emission to the environment. Recycling activity is taking place spontaneously by the informal pickers, leads to the difficulty in managing the whole system and uncertainty of the overall data. With a relative calculation, resulting in only approximately 0,17Mt CO2 equivalent emission, incinerator is suggested to be the solution of the problem with overloaded landfill and raising energy demand within the inhabitants.

Solid-state reference and ion-selective electrodes : towards portable potentiometric sensing

Potentiometric sensors are very attractive tools for chemical analysis because of their simplicity, low power consumption and low cost. They are extensively used in clinical diagnostics and in environmental monitoring. Modern applications of both fields require improvements in the conventional construction and in the performance of the potentiometric sensors, as the trends are towards portable, on-site diagnostics and autonomous sensing in remote locations. The aim of this PhD work was to improve some of the sensor properties that currently hamper the implementation of the potentiometric sensors in modern applications. The first part of the work was concentrated on the development of a solid-state reference electrode (RE) compatible with already existing solid-contact ion-selective electrodes (ISE), both of which are needed for all-solid-state potentiometric sensing systems. A poly(vinyl chloride) membrane doped with a moderately lipophilic salt, tetrabutylammonium-tetrabutylborate (TBA-TBB), was found to show a satisfactory stability of potential in sample solutions with different concentrations. Its response time was nevertheless slow, as it required several minutes to reach the equilibrium. The TBA-TBB membrane RE worked well together with solid-state ISEs in several different situations and on different substrates enabling a miniature design. Solid contacts (SC) that mediate the ion-to-electron transduction are crucial components of well-functioning potentiometric sensors. This transduction process converting the ionic conduction of an ion-selective membrane to the electronic conduction in the circuit was studied with the help of electrochemical impedance spectroscopy (EIS). The solid contacts studied were (i) the conducting polymer (CP) poly(3,4-ethylienedioxythiophene) (PEDOT) and (ii) a carbon cloth having a high surface area. The PEDOT films were doped with a large immobile anion poly(styrene sulfonate) (PSS-) or with a small mobile anion Cl-. As could be expected, the studied PEDOT solid-contact mediated the ion-toelectron transduction more efficiently than the bare glassy carbon substrate, onto which they were electropolymerized, while the impedance of the PEDOT films depended on the mobility of the doping ion and on the ions in the electrolyte. The carbon cloth was found to be an even more effective ion-to-electron transducer than the PEDOT films and it also proved to work as a combined electrical conductor and solid contact when covered with an ion-selective membrane or with a TBA-TBB-based reference membrane. The last part of the work was focused on improving the reproducibility and the potential stability of the SC-ISEs, a problem that culminates to the stability of the standard potential E°. It was proven that the E° of a SC-ISE with a conducting polymer as a solid contact could be adjusted by reducing or oxidizing the CP solid contact by applying current pulses or a potential to it, as the redox state of the CP solid-contact influences the overall potential of the ISE. The slope and thus the analytical performance of the SC-ISEs were retained despite the adjustment of the E°. The shortcircuiting of the SC-ISE with a conventional large-capacitance RE was found to be a feasible instrument-free method to control the E°. With this method, the driving force for the oxidation/reduction of the CP was the potential difference between the RE and the SC-ISE, and the position of the adjusted potential could be controlled by choosing a suitable concentration for the short-circuiting electrolyte. The piece-to-piece reproducibility of the adjusted potential was promising, and the day-today reproducibility for a specific sensor was excellent. The instrumentfree approach to control the E° is very attractive considering practical applications.