Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Cuticular and Suberin Polymers of Edible Plants. Analysis by Gas Chromatographic-Mass Spectrometric and Solid State Spectroscopic Methods

Cutin and suberin are structural and protective polymers of plant surfaces. The epidermal cells of the aerial parts of plants are covered with an extracellular cuticular layer, which consists of polyester cutin, highly resistant cutan, cuticular waxes and polysaccharides which link the layer to the epidermal cells. A similar protective layer is formed by a polyaromatic-polyaliphatic biopolymer suberin, which is present particularly in the cell walls of the phellem layer of periderm of the underground parts of plants (e.g. roots and tubers) and the bark of trees. In addition, suberization is also a major factor in wound healing and wound periderm formation regardless of the plants’ tissue. Knowledge of the composition and functions of cuticular and suberin polymers is important for understanding the physiological properties for the plants and for nutritional quality when these plants are consumed as foods. The aims of the practical work were to assess the chemical composition of cuticular polymers of several northern berries and seeds and suberin of two varieties of potatoes. Cutin and suberin were studied as isolated polymers and further after depolymerization as soluble monomers and solid residues. Chemical and enzymatic depolymerization techniques were compared and a new chemical depolymerization method was developed. Gas chromatographic analysis with mass spectrometric detection (GC-MS) was used to assess the monomer compositions. Polymer investigations were conducted with solid state carbon-13 cross polarization magic angle spinning nuclear magnetic resonance spectroscopy (13C CP-MAS NMR), Fourier transform infrared spectroscopy (FTIR) and microscopic analysis. Furthermore, the development of suberin over one year of post-harvest storage was investigated and the cuticular layers from berries grown in the North and South of Finland were compared. The results show that the amounts of isolated cuticular layers and cutin monomers, as well as monomeric compositions vary greatly between the berries. The monomer composition of seeds was found to differ from the corresponding berry peel monomers. The berry cutin monomers were composed mostly of long-chain aliphatic ω-hydroxy acids, with various mid-chain functionalities (double-bonds, epoxy, hydroxy and keto groups). Substituted α,ω-diacids predominated over ω-hydroxy acids in potato suberin monomers and slight differences were found between the varieties. The newly-developed closed tube chemical method was found to be suitable for cutin and suberin analysis and preferred over the solvent-consuming and laborious reflux method. Enzymatic hydrolysis with cutinase was less effective than chemical methanolysis and showed specificity towards α,ω-diacid bonds. According to ₁₃C CP-MAS NMR and FTIR, the depolymerization residues contained significant amounts of aromatic structures, polysaccharides and possible cutan-type aliphatic moieties. Cultivation location seems to have effect on cuticular composition. The materials studied contained significant amounts of different types of biopolymers that could be utilized for several purposes with or without further processing. The importance of the so-called waste material from industrial processes of berries and potatoes as a source of either dietary fiber or specialty chemicals should be further investigated in detail. The evident impact of cuticular and suberin polymers, among other fiber components, on human health should be investigated in clinical trials. These by-product materials may be used as value-added fiber fractions in the food industry and as raw materials for specialty chemicals such as lubricants and emulsifiers, or as building blocks for novel polymers.

Spectroscopic monitoring during laser welding of aluminium alloy

The mechanical properties of aluminium alloys are strongly influenced by the alloying elements and their concentration. In the case of aluminium alloy EN AW-6060 the main alloying elements are magnesium and silicon. The first goal of this thesis was to determine stability, repeatability and sensitivity as figures of merit of the in-situ melt identification technique. In this study the emissions from the laser welding process were monitored with a spectrometer. With the information produced by the spectrometer, quantitative analysis was conducted to determine the figures of merit. The quantitative analysis concentrated on magnesium and aluminium emissions and their relation. The results showed that the stability of absolute intensities was low, but the normalized magnesium emissions were quite stable. The repeatability of monitoring magnesium emissions was high (about 90 %). Sensitivity of the in-situ melt identification technique was also high. As small as 0.5 % change in magnesium content was detected by the spectrometer. The second goal of this study was to determine the loss of mass during deep penetration laser welding. The amount of magnesium in the material was measured before and after laser welding to determine the loss of magnesium. This study was conducted for aluminium alloy with nominal magnesium content of 0-10 % and for standard material EN AW-6060 that was welded with filler wire AlMg5. It was found that while the magnesium concentration in the material changed, the loss of magnesium remained fairly even. Also by feeding filler wire, the behaviour was similar. Thirdly, the reason why silicon had not been detected in the emission spectrum needed to be explained. Literature research showed that the amount of energy required for silicon to excite is considerably higher compared to magnesium. The energy input in the used welding process is insufficient to excite the silicon atoms.

Test Campaign Parameter Editor for a Graphical TTCN-3 Development Environment

This paper presents the design for a graphical parameter editor for Testing and Test Control Notation 3 (TTCN-3) test suites. This work was done in the context of OpenTTCN IDE, a TTCN-3 development environment built on top of the Eclipse platform. The design presented relies on an additional parameter editing tab added to the launch configurations for test campaigns. This parameter editing tab shows the list of editable parameters and allows opening editing components for the different parameters. Each TTCN-3 primitive type will have a specific editing component providing tools to ease modification of values of that type.

Differential Evolution approach and parameter estimation of chaotic

Parameter estimation still remains a challenge in many important applications. There is a need to develop methods that utilize achievements in modern computational systems with growing capabilities. Owing to this fact different kinds of Evolutionary Algorithms are becoming an especially perspective field of research. The main aim of this thesis is to explore theoretical aspects of a specific type of Evolutionary Algorithms class, the Differential Evolution (DE) method, and implement this algorithm as codes capable to solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation empirically demonstrates the benefits of a stochastic optimizers with respect to deterministic optimizers in case of stochastic and chaotic problems. Furthermore, the advanced features of Differential Evolution are discussed as well as taken into account in the Matlab realization. Test "toycase" examples are presented in order to show advantages and disadvantages caused by additional aspects involved in extensions of the basic algorithm. Another aim of this paper is to apply the DE approach to the parameter estimation problem of the system exhibiting chaotic behavior, where the well-known Lorenz system with specific set of parameter values is taken as an example. Finally, the DE approach for estimation of chaotic dynamics is compared to the Ensemble prediction and parameter estimation system (EPPES) approach which was recently proposed as a possible solution for similar problems.

Novel Methods for Error Modeling and Parameter Identification of a Redundant Serial-Parallel Hybrid Robot

To obtain the desirable accuracy of a robot, there are two techniques available. The first option would be to make the robot match the nominal mathematic model. In other words, the manufacturing and assembling tolerances of every part would be extremely tight so that all of the various parameters would match the “design” or “nominal” values as closely as possible. This method can satisfy most of the accuracy requirements， but the cost would increase dramatically as the accuracy requirement increases. Alternatively, a more cost-effective solution is to build a manipulator with relaxed manufacturing and assembling tolerances. By modifying the mathematical model in the controller, the actual errors of the robot can be compensated. This is the essence of robot calibration. Simply put, robot calibration is the process of defining an appropriate error model and then identifying the various parameter errors that make the error model match the robot as closely as possible. This work focuses on kinematic calibration of a 10 degree-of-freedom (DOF) redundant serial-parallel hybrid robot. The robot consists of a 4-DOF serial mechanism and a 6-DOF hexapod parallel manipulator. The redundant 4-DOF serial structure is used to enlarge workspace and the 6-DOF hexapod manipulator is used to provide high load capabilities and stiffness for the whole structure. The main objective of the study is to develop a suitable calibration method to improve the accuracy of the redundant serial-parallel hybrid robot. To this end, a Denavit–Hartenberg (DH) hybrid error model and a Product-of-Exponential (POE) error model are developed for error modeling of the proposed robot. Furthermore, two kinds of global optimization methods, i.e. the differential-evolution (DE) algorithm and the Markov Chain Monte Carlo (MCMC) algorithm, are employed to identify the parameter errors of the derived error model. A measurement method based on a 3-2-1 wire-based pose estimation system is proposed and implemented in a Solidworks environment to simulate the real experimental validations. Numerical simulations and Solidworks prototype-model validations are carried out on the hybrid robot to verify the effectiveness, accuracy and robustness of the calibration algorithms.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Modeling and Parameter Estimation of Double-Star Permanent Magnet Synchronous Machines

The power rating of wind turbines is constantly increasing; however, keeping the voltage rating at the low-voltage level results in high kilo-ampere currents. An alternative for increasing the power levels without raising the voltage level is provided by multiphase machines. Multiphase machines are used for instance in ship propulsion systems, aerospace applications, electric vehicles, and in other high-power applications including wind energy conversion systems. A machine model in an appropriate reference frame is required in order to design an efficient control for the electric drive. Modeling of multiphase machines poses a challenge because of the mutual couplings between the phases. Mutual couplings degrade the drive performance unless they are properly considered. In certain multiphase machines there is also a problem of high current harmonics, which are easily generated because of the small current path impedance of the harmonic components. However, multiphase machines provide special characteristics compared with the three-phase counterparts: Multiphase machines have a better fault tolerance, and are thus more robust. In addition, the controlled power can be divided among more inverter legs by increasing the number of phases. Moreover, the torque pulsation can be decreased and the harmonic frequency of the torque ripple increased by an appropriate multiphase configuration. By increasing the number of phases it is also possible to obtain more torque per RMS ampere for the same volume, and thus, increase the power density. In this doctoral thesis, a decoupled d–q model of double-star permanent-magnet (PM) synchronous machines is derived based on the inductance matrix diagonalization. The double-star machine is a special type of multiphase machines. Its armature consists of two three-phase winding sets, which are commonly displaced by 30 electrical degrees. In this study, the displacement angle between the sets is considered a parameter. The diagonalization of the inductance matrix results in a simplified model structure, in which the mutual couplings between the reference frames are eliminated. Moreover, the current harmonics are mapped into a reference frame, in which they can be easily controlled. The work also presents methods to determine the machine inductances by a finite-element analysis and by voltage-source inverters on-site. The derived model is validated by experimental results obtained with an example double-star interior PM (IPM) synchronous machine having the sets displaced by 30 electrical degrees. The derived transformation, and consequently, the decoupled d–q machine model, are shown to model the behavior of an actual machine with an acceptable accuracy. Thus, the proposed model is suitable to be used for the model-based control design of electric drives consisting of double-star IPM synchronous machines.

Spectroscopic Studies of III-V Semiconductor Materials for Improved Devices

Defects in semiconductor crystals and at their interfaces usually impair the properties and the performance of devices. These defects include, for example, vacancies (i.e., missing crystal atoms), interstitials (i.e., extra atoms between the host crystal sites), and impurities such as oxygen atoms. The defects can decrease (i) the rate of the radiative electron transition from the conduction band to the valence band, (ii) the amount of charge carriers, and (iii) the mobility of the electrons in the conduction band. It is a common situation that the presence of crystal defects can be readily concluded as a decrease in the luminescence intensity or in the current flow for example. However, the identification of the harmful defects is not straightforward at all because it is challenging to characterize local defects with atomic resolution and identification. Such atomic-scale knowledge is however essential to find methods for reducing the amount of defects in energy-efficient semiconductor devices. The defects formed in thin interface layers of semiconductors are particularly difficult to characterize due to their buried and amorphous structures. Characterization methods which are sensitive to defects often require well-defined samples with long range order. Photoelectron spectroscopy (PES) combined with photoluminescence (PL) or electrical measurements is a potential approach to elucidate the structure and defects of the interface. It is essential to combine the PES with complementary measurements of similar samples to relate the PES changes to changes in the interface defect density. Understanding of the nature of defects related to III-V materials is relevant to developing for example field-effect transistors which include a III-V channel, but research is still far from complete. In this thesis, PES measurements are utilized in studies of various III-V compound semiconductor materials. PES is combined with photoluminescence measurements to study the SiO2/GaAs, SiNx/GaAs and BaO/GaAs interfaces. Also the formation of novel materials InN and photoluminescent GaAs nanoparticles are studied. Finally, the formation of Ga interstitial defects in GaAsN is elucidated by combining calculational results with PES measurements.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.