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.

Accuracy improvement of a demand forecasting model

This research concerns different statistical methods that assist to increase the demand forecasting accuracy of company X’s forecasting model. Current forecasting process was analyzed in details. As a result, graphical scheme of logical algorithm was developed. Based on the analysis of the algorithm and forecasting errors, all the potential directions for model future improvements in context of its accuracy were gathered into the complete list. Three improvement directions were chosen for further practical research, on their basis, three test models were created and verified. Novelty of this work lies in the methodological approach of the original analysis of the model, which identified its critical points, as well as the uniqueness of the developed test models. Results of the study formed the basis of the grant of the Government of St. Petersburg.

Spatiotemporal Features of Coastal Waters in Southwest Finland

In coastal waters, physico-chemical and biological properties and constituents vary at different time scales. In the study area of this thesis, within the Archipelago Sea in the northern Baltic Sea, seasonal cycles of light and temperature set preconditions for intra-annual variations, but developments at other temporal scales occur as well. Weather-induced runoffs and currents may alter water properties over the short term, and the consequences over time of eutrophication and global changes are to a degree unpredictable. The dynamic characteristics of northern Baltic Sea waters are further diversified at the archipelago coasts. Water properties may differ in adjacent basins, which are separated by island and underwater thresholds limiting water exchange, making the area not only a mosaic of islands but also one of water masses. Long-term monitoring and in situ observations provide an essential data reserve for coastal management and research. Since the seasonal amplitudes of water properties are so high, inter-annual comparisons of water-quality variables have to be based on observations sampled at the same time each year. In this thesis I compare areas by their temporal characteristics, using both inter-annual and seasonal data. After comparing spatial differences in seasonal cycles, I conclude that spatial comparisons and temporal generalizations have to be made with caution. In classifying areas by the state of their waters, the results may be biased even if the sampling is annually simultaneous, since the dynamics of water properties may vary according to the area. The most comprehensive view of the spatiotemporal dynamics of water properties would be achieved by means of comparisons with data consisting of multiple annual samples. For practical reasons, this cannot be achieved with conventional in situ sampling. A holistic understanding of the spatiotemporal features of the water properties of the Archipelago Sea will have to be based on the application of multiple methods, complementing each other’s spatial and temporal coverage. The integration of multi-source observational data and time-series analysis may be methodologically challenging, but it will yield new information as to the spatiotemporal regime of the Archipelago Sea.

Ionsonde Measurement Trend

Time series analysis has gone through different developmental stages before the current modern approaches. These can broadly categorized as the classical time series analysis and modern time series analysis approach. In the classical one, the basic target of the analysis is to describe the major behaviour of the series without necessarily dealing with the underlying structures. On the contrary, the modern approaches strives to summarize the behaviour of the series going through its underlying structure so that the series can be represented explicitly. In other words, such approach of time series analysis tries to study the series structurally. The components of the series that make up the observation such as the trend, seasonality, regression and disturbance terms are modelled explicitly before putting everything together in to a single state space model which give the natural interpretation of the series. The target of this diploma work is to practically apply the modern approach of time series analysis known as the state space approach, more specifically, the dynamic linear model, to make trend analysis over Ionosonde measurement data. The data is time series of the peak height of F2 layer symbolized by hmF2 which is the height of high electron density. In addition, the work also targets to investigate the connection between solar activity and the peak height of F2 layer. Based on the result found, the peak height of the F2 layer has shown a decrease during the observation period and also shows a nonlinear positive correlation with solar activity.

Simulation of structural stress history based on dynamic analysis

Modern machine structures are often fabricated by welding. From a fatigue point of view, the structural details and especially, the welded details are the most prone to fatigue damage and failure. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the stress loads that act on each detail. Even though, dynamic simulation of flexible bodies is already current method for analyzing structures, obtaining the stress history of a structural detail during dynamic simulation is a challenging task; especially when the detail has a complex geometry. In particular, analyzing the stress history of every structural detail within a single finite element model can be overwhelming since the amount of nodal degrees of freedom needed in the model may require an impractical amount of computational effort. The purpose of computer simulation is to reduce amount of prototypes and speed up the product development process. Also, to take operator influence into account, real time models, i.e. simplified and computationally efficient models are required. This in turn, requires stress computation to be efficient if it will be performed during dynamic simulation. The research looks back at the theoretical background of multibody dynamic simulation and finite element method to find suitable parts to form a new approach for efficient stress calculation. This study proposes that, the problem of stress calculation during dynamic simulation can be greatly simplified by using a combination of floating frame of reference formulation with modal superposition and a sub-modeling approach. In practice, the proposed approach can be used to efficiently generate the relevant fatigue assessment stress history for a structural detail during or after dynamic simulation. In this work numerical examples are presented to demonstrate the proposed approach in practice. The results show that approach is applicable and can be used as proposed.

National oral history - Time of change project

Reviews

Survival-time analysis of white spruce during spruce budworm defoliation

Abstract

Performance analysis of software run-time behaviour using 3D-visualisation

Monimutkaisen tietokonejärjestelmän suorituskykyoptimointi edellyttää järjestelmän ajonaikaisen käyttäytymisen ymmärtämistä. Ohjelmiston koon ja monimutkaisuuden kasvun myötä suorituskykyoptimointi tulee yhä tärkeämmäksi osaksi tuotekehitysprosessia. Tehokkaampien prosessorien käytön myötä myös energiankulutus ja lämmöntuotto ovat nousseet yhä suuremmiksi ongelmiksi, erityisesti pienissä, kannettavissa laitteissa. Lämpö- ja energiaongelmien rajoittamiseksi on kehitetty suorituskyvyn skaalausmenetelmiä, jotka edelleen lisäävät järjestelmän kompleksisuutta ja suorituskykyoptimoinnin tarvetta. Tässä työssä kehitettiin visualisointi- ja analysointityökalu ajonaikaisen käyttäytymisen ymmärtämisen helpottamiseksi. Lisäksi kehitettiin suorituskyvyn mitta, joka mahdollistaa erilaisten skaalausmenetelmien vertailun ja arvioimisen suoritusympäristöstä riippumatta, perustuen joko suoritustallenteen tai teoreettiseen analyysiin. Työkalu esittää ajonaikaisesti kerätyn tallenteen helposti ymmärrettävällä tavalla. Se näyttää mm. prosessit, prosessorikuorman, skaalausmenetelmien toiminnan sekä energiankulutuksen kolmiulotteista grafiikkaa käyttäen. Työkalu tuottaa myös käyttäjän valitsemasta osasta suorituskuvaa numeerista tietoa, joka sisältää useita oleellisia suorituskykyarvoja ja tilastotietoa. Työkalun sovellettavuutta tarkasteltiin todellisesta laitteesta saatua suoritustallennetta sekä suorituskyvyn skaalauksen simulointia analysoimalla. Skaalausmekanismin parametrien vaikutus simuloidun laitteen suorituskykyyn analysoitiin.

Using time and stochastic models for software reliability forecasting and analysis

Tämä työ luo katsauksen ajallisiin ja stokastisiin ohjelmien luotettavuus malleihin sekä tutkii muutamia malleja käytännössä. Työn teoriaosuus sisältää ohjelmien luotettavuuden kuvauksessa ja arvioinnissa käytetyt keskeiset määritelmät ja metriikan sekä varsinaiset mallien kuvaukset. Työssä esitellään kaksi ohjelmien luotettavuusryhmää. Ensimmäinen ryhmä ovat riskiin perustuvat mallit. Toinen ryhmä käsittää virheiden ”kylvöön” ja merkitsevyyteen perustuvat mallit. Työn empiirinen osa sisältää kokeiden kuvaukset ja tulokset. Kokeet suoritettiin käyttämällä kolmea ensimmäiseen ryhmään kuuluvaa mallia: Jelinski-Moranda mallia, ensimmäistä geometrista mallia sekä yksinkertaista eksponenttimallia. Kokeiden tarkoituksena oli tutkia, kuinka syötetyn datan distribuutio vaikuttaa mallien toimivuuteen sekä kuinka herkkiä mallit ovat syötetyn datan määrän muutoksille. Jelinski-Moranda malli osoittautui herkimmäksi distribuutiolle konvergaatio-ongelmien vuoksi, ensimmäinen geometrinen malli herkimmäksi datan määrän muutoksille.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.

Analysis of patterns in mining time series using Qlucore

Raw measurement data does not always immediately convey useful information, but applying mathematical statistical analysis tools into measurement data can improve the situation. Data analysis can offer benefits like acquiring meaningful insight from the dataset, basing critical decisions on the findings, and ruling out human bias through proper statistical treatment. In this thesis we analyze data from an industrial mineral processing plant with the aim of studying the possibility of forecasting the quality of the final product, given by one variable, with a model based on the other variables. For the study mathematical tools like Qlucore Omics Explorer (QOE) and Sparse Bayesian regression (SB) are used. Later on, linear regression is used to build a model based on a subset of variables that seem to have most significant weights in the SB model. The results obtained from QOE show that the variable representing the desired final product does not correlate with other variables. For SB and linear regression, the results show that both SB and linear regression models built on 1-day averaged data seriously underestimate the variance of true data, whereas the two models built on 1-month averaged data are reliable and able to explain a larger proportion of variability in the available data, making them suitable for prediction purposes. However, it is concluded that no single model can fit well the whole available dataset and therefore, it is proposed for future work to make piecewise non linear regression models if the same available dataset is used, or the plant to provide another dataset that should be collected in a more systematic fashion than the present data for further analysis.

MCMC Analysis Of Classical Time Series Algorithms

Identification of order of an Autoregressive Moving Average Model (ARMA) by the usual graphical method is subjective. Hence, there is a need of developing a technique to identify the order without employing the graphical investigation of series autocorrelations. To avoid subjectivity, this thesis focuses on determining the order of the Autoregressive Moving Average Model using Reversible Jump Markov Chain Monte Carlo (RJMCMC). The RJMCMC selects the model from a set of the models suggested by better fitting, standard deviation errors and the frequency of accepted data. Together with deep analysis of the classical Box-Jenkins modeling methodology the integration with MCMC algorithms has been focused through parameter estimation and model fitting of ARMA models. This helps to verify how well the MCMC algorithms can treat the ARMA models, by comparing the results with graphical method. It has been seen that the MCMC produced better results than the classical time series approach.

Analysis of Patterns in Electricity Spot Market Time Series

Due to its non-storability, electricity must be produced at the same time that it is consumed, as a result prices are determined on an hourly basis and thus analysis becomes more challenging. Moreover, the seasonal fluctuations in demand and supply lead to a seasonal behavior of electricity spot prices. The purpose of this thesis is to seek and remove all causal effects from electricity spot prices and remain with pure prices for modeling purposes. To achieve this we use Qlucore Omics Explorer (QOE) for the visualization and the exploration of the data set and Time Series Decomposition method to estimate and extract the deterministic components from the series. To obtain the target series we use regression based on the background variables (water reservoir and temperature). The result obtained is three price series (for Sweden, Norway and System prices) with no apparent pattern.

Unca Don and Unca Scrooge’s Guide to History. Representations of the Past in the Disney Comics of Don Rosa

This thesis studies the various forms and layers of representations of the past that can be found in the Disney comics of Don Rosa. To stay true to the legacy of renowned comic book artist Carl Barks, Rosa has stopped time in the duck universe to the 1950’s: the decade when Barks created his most noted stories. There is a special feel of historicalness in Rosa’s duck stories, as his characters recall events that occurred in both Rosa’s own stories as well as Barks’. Rosa has shed new light to the past of the characters by writing and illustrating the history of Scrooge McDuck, one of the most beloved Disney characters. Rosa is also adamant that the historical facts used in his stories are always correct and based on thorough research. The methodological tools used in the analysis of the comics come from the fields of comic book studies, film theory, and history culture. Film and comics are recognized by many scholars as very similar media, which share elements that make them comparable in many ways. This thesis utilizes studies on historical film, narrative and genre, which provide valuable insight and comparisons for analysis. The thesis consists of three main chapters, the first of which deconstructs the duck universe in the stories in order to understand how the historicalness in them is created,and which outside elements might affect them, including the genre of Disney comics, publishers, and the legacy of Barks. The next chapter focuses on The Life and Times of Scrooge McDuck series, i.e. the stories which are located in the past. Such stories feature similar representations of history as for example Westerns. They also compress and alter history to meet the restrictions of the medium of comics. The last part focuses on the adventure stories which draw inspiration from for example mythology, and take the characters to strange and mystical, but yet historical worlds. Such treasure-hunting stories show similarity to the action-adventure genre in film and for example their stereotypical representations of foreign cultures. Finally, the chapter addresses the problematic of historical fiction and its capability to write history.

Time frames. Negotiating Cultural History

Time Frames brings together a group of cultural historians studying several different periods and locations in the history of Western culture, to discuss the temporal structures which historical studies live by. How do we construct chronologies and temporal sequences? How should we approach the discontinuity and particularity of the past, and its periodization? Deploying ideas and frames from three contemporary conceptual debates - spatial organisation, constructions of experience, and the cultural embeddedness of individual agency - the writers of this book propose methods of historicizing and explore what cultural history is about today.