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.

Quantile Estimation in Non-Stationary Streaming Data

We provide an incremental quantile estimator for Non-stationary Streaming Data. We propose a method for simultaneous estimation of multiple quantiles corresponding to the given probability levels from streaming data. Due to the limitations of the memory, it is not feasible to compute the quantiles by storing the data. So estimating the quantiles as the data pass by is the only possibility. This can be effective in network measurement. To provide the minimum of the mean-squared error of the estimation, we use parabolic approximation and for comparison we simulate the results for different number of runs and using both linear and parabolic approximations.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

Improving Dynamic Characteristics of Open-loop Controlled Log Crane

The improvement of the dynamics of flexible manipulators like log cranes often requires advanced control methods. This thesis discusses the vibration problems in the cranes used in commercial forestry machines. Two control methods, adaptive filtering and semi-active damping, are presented. The adaptive filter uses a part of the lowest natural frequency of the crane as a filtering frequency. The payload estimation algorithm, filtering of control signal and algorithm for calculation of the lowest natural frequency of the crane are presented. The semi-active damping method is basedon pressure feedback. The pressure vibration, scaled with suitable gain, is added to the control signal of the valve of the lift cylinder to suppress vibrations. The adaptive filter cuts off high frequency impulses coming from the operatorand semi-active damping suppresses the crane?s oscillation, which is often caused by some external disturbance. In field tests performed on the crane, a correctly tuned (25 % tuning) adaptive filter reduced pressure vibration by 14-17 % and semi-active damping correspondingly by 21-43%. Applying of these methods require auxiliary transducers, installed in specific points in the crane, and electronically controlled directional control valves.

Gas-liquid mass transfer in bubbly flow: Estimation of mass transfer, bubble size and reactor performance in various applications

Gas-liquid mass transfer is an important issue in the design and operation of many chemical unit operations. Despite its importance, the evaluation of gas-liquid mass transfer is not straightforward due to the complex nature of the phenomena involved. In this thesis gas-liquid mass transfer was evaluated in three different gas-liquid reactors in a traditional way by measuring the volumetric mass transfer coefficient (kLa). The studied reactors were a bubble column with a T-junction two-phase nozzle for gas dispersion, an industrial scale bubble column reactor for the oxidation of tetrahydroanthrahydroquinone and a concurrent downflow structured bed.The main drawback of this approach is that the obtained correlations give only the average volumetric mass transfer coefficient, which is dependent on average conditions. Moreover, the obtained correlations are valid only for the studied geometry and for the chemical system used in the measurements. In principle, a more fundamental approach is to estimate the interfacial area available for mass transfer from bubble size distributions obtained by solution of population balance equations. This approach has been used in this thesis by developing a population balance model for a bubble column together with phenomenological models for bubble breakage and coalescence. The parameters of the bubble breakage rate and coalescence rate models were estimated by comparing the measured and calculated bubble sizes. The coalescence models always have at least one experimental parameter. This is because the bubble coalescence depends on liquid composition in a way which is difficult to evaluate using known physical properties. The coalescence properties of some model solutions were evaluated by measuring the time that a bubble rests at the free liquid-gas interface before coalescing (the so-calledpersistence time or rest time). The measured persistence times range from 10 msup to 15 s depending on the solution. The coalescence was never found to be instantaneous. The bubble oscillates up and down at the interface at least a coupleof times before coalescence takes place. The measured persistence times were compared to coalescence times obtained by parameter fitting using measured bubble size distributions in a bubble column and a bubble column population balance model. For short persistence times, the persistence and coalescence times are in good agreement. For longer persistence times, however, the persistence times are at least an order of magnitude longer than the corresponding coalescence times from parameter fitting. This discrepancy may be attributed to the uncertainties concerning the estimation of energy dissipation rates, collision rates and mechanisms and contact times of the bubbles.

On Effort Estimation in Software Projects

Software engineering is criticized as not being engineering or 'well-developed' science at all. Software engineers seem not to know exactly how long their projects will last, what they will cost, and will the software work properly after release. Measurements have to be taken in software projects to improve this situation. It is of limited use to only collect metrics afterwards. The values of the relevant metrics have to be predicted, too. The predictions (i.e. estimates) form the basis for proper project management. One of the most painful problems in software projects is effort estimation. It has a clear and central effect on other project attributes like cost and schedule, and to product attributes like size and quality. Effort estimation can be used for several purposes. In this thesis only the effort estimation in software projects for project management purposes is discussed. There is a short introduction to the measurement issues, and some metrics relevantin estimation context are presented. Effort estimation methods are covered quite broadly. The main new contribution in this thesis is the new estimation model that has been created. It takes use of the basic concepts of Function Point Analysis, but avoids the problems and pitfalls found in the method. It is relativelyeasy to use and learn. Effort estimation accuracy has significantly improved after taking this model into use. A major innovation related to the new estimationmodel is the identified need for hierarchical software size measurement. The author of this thesis has developed a three level solution for the estimation model. All currently used size metrics are static in nature, but this new proposed metric is dynamic. It takes use of the increased understanding of the nature of the work as specification and design work proceeds. It thus 'grows up' along with software projects. The effort estimation model development is not possible without gathering and analyzing history data. However, there are many problems with data in software engineering. A major roadblock is the amount and quality of data available. This thesis shows some useful techniques that have been successful in gathering and analyzing the data needed. An estimation process is needed to ensure that methods are used in a proper way, estimates are stored, reported and analyzed properly, and they are used for project management activities. A higher mechanism called measurement framework is also introduced shortly. The purpose of the framework is to define and maintain a measurement or estimationprocess. Without a proper framework, the estimation capability of an organization declines. It requires effort even to maintain an achieved level of estimationaccuracy. Estimation results in several successive releases are analyzed. It isclearly seen that the new estimation model works and the estimation improvementactions have been successful. The calibration of the hierarchical model is a critical activity. An example is shown to shed more light on the calibration and the model itself. There are also remarks about the sensitivity of the model. Finally, an example of usage is shown.

Cost Estimation of Engineering Environment Services

Työn tavoitteena oli kehittää tutkittavan insinööriyksikön projektien kustannusestimointiprosessia, siten että yksikön johdolla olisi tulevaisuudessa käytettävänään tarkempaa kustannustietoa. Jotta tämä olisi mahdollista, ensin täytyi selvittää yksikön toimintatavat, projektien kustannusrakenteet sekä kustannusatribuutit. Tämän teki mahdolliseksi projektien kustannushistoriatiedon tutkiminen sekä asiantuntijoiden haastattelu. Työn tuloksena syntyi kohdeyksikön muiden prosessien kanssa yhteensopiva kustannusestimointiprosessi sekä –malli.Kustannusestimointimenetelmän ja –mallin perustana on kustannusatribuutit, jotka määritellään erikseen tutkittavassa ympäristössä. Kustannusatribuutit löydetään historiatietoa tutkimalla, eli analysoimalla jo päättyneitä projekteja, projektien kustannusrakenteita sekä tekijöitä, jotka ovat vaikuttaneet kustannusten syntyyn. Tämän jälkeen kustannusatribuuteille täytyy määritellä painoarvot sekä painoarvojen vaihteluvälit. Estimointimallin tarkuutta voidaan parantaa mallin kalibroinnilla. Olen käyttänyt Goal – Question – Metric (GQM) –menetelmää tutkimuksen kehyksenä.

Bayesian Estimation of Noise

In mathematical modeling the estimation of the model parameters is one of the most common problems. The goal is to seek parameters that fit to the measurements as well as possible. There is always error in the measurements which implies uncertainty to the model estimates. In Bayesian statistics all the unknown quantities are presented as probability distributions. If there is knowledge about parameters beforehand, it can be formulated as a prior distribution. The Bays’ rule combines the prior and the measurements to posterior distribution. Mathematical models are typically nonlinear, to produce statistics for them requires efficient sampling algorithms. In this thesis both Metropolis-Hastings (MH), Adaptive Metropolis (AM) algorithms and Gibbs sampling are introduced. In the thesis different ways to present prior distributions are introduced. The main issue is in the measurement error estimation and how to obtain prior knowledge for variance or covariance. Variance and covariance sampling is combined with the algorithms above. The examples of the hyperprior models are applied to estimation of model parameters and error in an outlier case.

Modeling reaction kinetics and mass transfer in ozonation in water solutions

This dissertation is based on four articles dealing with modeling of ozonation. The literature part of this considers some models for hydrodynamics in bubble column simulation. A literature review of methods for obtaining mass transfer coefficients is presented. The methods presented to obtain mass transfer are general models and can be applied to any gas-liquid system. Ozonation reaction models and methods for obtaining stoichiometric coefficients and reaction rate coefficients for ozonation reactions are discussed in the final section of the literature part. In the first article, ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. A more general method for estimation of mass transfer and Henry’s coefficient was developed from the Beltrán method. The ozone volumetric mass transfer coefficient and the Henry’s coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A minor dependence of the Henry’s law constant on pH was detected at the pH range 4 - 9. In the second article, a new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semi-batch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with the literature data. The reaction order in the pH range 7-10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. Sensitivity analysis was conducted using object function method to obtain information about the reliability and identifiability of the estimated parameters. In the third article, the reaction rate coefficients and the stoichiometric coefficients in the reaction of ozone with the model component p-nitrophenol were estimated at low pH of water using nonlinear optimization. A novel method for estimation of multireaction model parameters in ozonation was developed. In this method the concentration of unknown intermediate compounds is presented as a residual COD (chemical oxygen demand) calculated from the measured COD and the theoretical COD for the known species. The decomposition rate of p-nitrophenol on the pathway producing hydroquinone was found to be about two times faster than the p-nitrophenol decomposition rate on the pathway producing 4- nitrocatechol. In the fourth article, the reaction kinetics of p-nitrophenol ozonation was studied in a bubble column at pH 2. Using the new reaction kinetic model presented in the previous article, the reaction kinetic parameters, rate coefficients, and stoichiometric coefficients as well as the mass transfer coefficient were estimated with nonlinear estimation. The decomposition rate of pnitrophenol was found to be equal both on the pathway producing hydroquinone and on the path way producing 4-nitrocathecol. Comparison of the rate coefficients with the case at initial pH 5 indicates that the p-nitrophenol degradation producing 4- nitrocathecol is more selective towards molecular ozone than the reaction producing hydroquinone. The identifiability and reliability of the estimated parameters were analyzed with the Marcov chain Monte Carlo (MCMC) method. @All rights reserved. No part of the publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the author.

Cost estimation framework for modular product

Cost estimation is an important, but challenging process when designing a new product or a feature of it, verifying the product prices given by suppliers or planning a cost saving actions of existing products. It is even more challenging when the product is highly modular, not a bulk product. In general, cost estimation techniques can be divided into two main groups - qualitative and quantitative techniques - which can further be classified into more detailed methods. Generally, qualitative techniques are preferable when comparing alternatives and quantitative techniques when cost relationships can be found. The main objective of this thesis was to develop a method on how to estimate costs of internally manufactured and commercial elevator landing doors. Because of the challenging product structure, the proposed cost estimation framework is developed under three different levels based on past cost information available. The framework consists of features from both qualitative and quantitative cost estimation techniques. The starting point for the whole cost estimation process is an unambiguous, hierarchical product structure so that the product can be classified into controllable parts and is then easier to handle. Those controllable parts can then be compared to existing past cost knowledge of similar parts and create as accurate cost estimates as possible by that way.

Sensor Fusion of Proprioception, Force and Vision in Estimation and Robot

Sensor-based robot control allows manipulation in dynamic environments with uncertainties. Vision is a versatile low-cost sensory modality, but low sample rate, high sensor delay and uncertain measurements limit its usability, especially in strongly dynamic environments. Force is a complementary sensory modality allowing accurate measurements of local object shape when a tooltip is in contact with the object. In multimodal sensor fusion, several sensors measuring different modalities are combined to give a more accurate estimate of the environment. As force and vision are fundamentally different sensory modalities not sharing a common representation, combining the information from these sensors is not straightforward. In this thesis, methods for fusing proprioception, force and vision together are proposed. Making assumptions of object shape and modeling the uncertainties of the sensors, the measurements can be fused together in an extended Kalman filter. The fusion of force and visual measurements makes it possible to estimate the pose of a moving target with an end-effector mounted moving camera at high rate and accuracy. The proposed approach takes the latency of the vision system into account explicitly, to provide high sample rate estimates. The estimates also allow a smooth transition from vision-based motion control to force control. The velocity of the end-effector can be controlled by estimating the distance to the target by vision and determining the velocity profile giving rapid approach and minimal force overshoot. Experiments with a 5-degree-of-freedom parallel hydraulic manipulator and a 6-degree-of-freedom serial manipulator show that integration of several sensor modalities can increase the accuracy of the measurements significantly.