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.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Aktiivisen verkkosillan tuottaman yhteismuotoisen jännitteen vaimentaminen kaksitasoisessa, jännitevälipiirillisessä, taajuusmuuttajatopologiassa

Pulssinleveysmoduloidun vaihtosuuntaajan hyötysuhteen parantaminen ja kytkentätaajuuden suurentaminen ovat johtaneet lähtöjännitteen suuritaajuiseen taajuussisältöön kaksitasoisessa, jännitevälipiirillisessä taajuusmuuttajatopologiassa. Kasvava tarve siirtää tehoa myös verkkoon päin on lisännyt aktiivisen verkkosillan käyttöä. Kaksitasoisen aktiivisen verkkosillan vaikutuksesta DC-välipiirin keskipisteen ja kolmivaiheisen kuorman tähtipisteen välinen jännite on nollasta poikkeava aiheuttaen suurentuneen yhteismuotoisen jännitteen taajuusmuuttajan lähtöön ja verkon puolelle. Lisäksi yhteismuotoisten jännitteiden aiheuttamat kytkentätaajuiset häiriövirrat voivat aiheuttaa vikavirtasuojien tahatonta laukeamista, vaikeuttaa EMC-standardien vaatimusten täyttämistä, lisätä moottorin käämieristyksien rasitusta ja mahdollisuutta moottorin laakerivaurioille. Diplomityössä tutkitaan aktiivisen ja passiivisen verkkosillan tuottamaa yhteismuotoista jännitettä simuloinneilla. Esitellään aikaisempaa tutkimustietoa yhteismuotoisen jännitteen ja virran vaimennusratkaisuista aktiivista verkkosiltaa käytettäessä. Tutkimustiedon pohjalta suunnitellaan koelaitteistolle soveltuva suodin. Suotimen toiminta testataan simuloinnein sekä kokeellisin mittauksin. Tehdyt mittaukset osoittavat, että suunniteltu suodin vaimentaa yhteismuotoista jännitettä noin 20 dB verkkosillan kytkentätaajuudella ja tämän jälkeen yli 20 dB/dekadi taajuuteen 100 kHz asti. Lisäksi yhteismuotoisen virran suuruus syöttökaapelin kautta pieneni ehdotetun suotimen vaikutuksesta.

Limittelymenetelmän hyödyntäminen verkkovaihtosuuntaajassa: LCL-suotimen mitoitus

Teollisuudessa yleinen trendi on saada entistä tehokkaampia, halvempia, hyötysuhteeltaan parempia ja fyysisiltä mitoiltaan pienempiä sähkökäyttöjä. Luonnollisesti nämä vaatimukset ovat samoja myös taajuusmuuttajilla. Näiden vaatimusten välillä täytyy aina tehdä kompromisseja ja kehittää uusia menetelmiä. Monissa teollisuuden sähkökäytöissä tarvitaan verkkovaihtosuuntaajaa syöttämään tehoa generaattorilta tai jarrutettavalta moottorilta sähköverkkoon. Verkkovaihtosuuntaajassa käytännössä tarvitaan aina LCL-suodin, joka on fyysisesti järjestelmän suurin ja kallein yksittäinen komponentti, ja luonnollisesti suuritehoinen laite vaatii suuren LCL-suotimen. LCL-Suotimen fyysinen koko on kääntäen verrannollinen kytkentätaajuuteen. Tässä diplomityössä esitellään interleaving eli limittelymenetelmä, jonka avulla pystytään kasvattamaan verkkovaihtosuuntaajan ekvivalenttista kytkentätaajuutta ja pienentämään virran värettä sekä kokonaisharmonista säröä. Menetelmästä aiheutuu myös merkittävä haaste, kiertovirrat, joiden suodatusta tutkitaan kahdella eri menetelmällä. Käytetyt suodatustavat ovat LCL-suodin, jossa on lisäksi CM-kuristin ja LCL-suodin, jossa käytetään solujen välistä muuntajaa, ICT:tä. Työ suoritettiin teoriatutkimuksena ja simuloimalla. Tulokset osoittavat, että molemmat suodatustavat voivat toimia todellisessa sovelluksessa. Kuitenkin vain ICT:n omaava suodin on selkeästi vastaavan kokoista kaksitasoista verkkovaihtosuuntaajan suodinta pienempi. Tutkimus osoittaa myös sen, että tutkitussa sovelluskohteessa pelkkä fyysinen suodin ei riitä suodattamaan kiertovirtoja, vaan säätimeen täytyy tehdä myös muutoksia.

Elasticsearch as a new search engine for Invenio and more

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Post-processing and analysis of tracked hand trajectories

In this thesis, the suitability of different trackers for finger tracking in high-speed videos was studied. Tracked finger trajectories from the videos were post-processed and analysed using various filtering and smoothing methods. Position derivatives of the trajectories, speed and acceleration were extracted for the purposes of hand motion analysis. Overall, two methods, Kernelized Correlation Filters and Spatio-Temporal Context Learning tracking, performed better than the others in the tests. Both achieved high accuracy for the selected high-speed videos and also allowed real-time processing, being able to process over 500 frames per second. In addition, the results showed that different filtering methods can be applied to produce more appropriate velocity and acceleration curves calculated from the tracking data. Local Regression filtering and Unscented Kalman Smoother gave the best results in the tests. Furthermore, the results show that tracking and filtering methods are suitable for high-speed hand-tracking and trajectory-data post-processing.

Radar cross-section measurement using the Doppler effect

In this Master Thesis we discuss issues related to the measurement of the effective scattering surface, based on the Doppler Effect. Modeling of the detected signal was made. Narrowband signal filtering using low-frequency amplifier was observed. Parameters of the proposed horn antennas were studied; radar cross section charts for three different objects were received.

Exhaled nitric oxide collected with two different mouthpieces: a study in asthmatic patients

Techniques for collecting exhaled nitric oxide (ENO) recommend the use of antibacterial filters of 0.3 µm. The aim of the present study was to compare the measurements of ENO obtained with two different filtering devices. Air samples from 17 asthmatic and 17 non-asthmatic subjects were collected by a recommended off-line technique using two different mouthpieces: 1) the Sievers disposable tool (A) under a breathing pressure of 18 cmH2O, and 2) a mouthpiece containing a HEPA filter (B) under a breathing pressure of 12 cmH2O. The nitric oxide samples were collected into an impermeable reservoir bag. Values for ENO were compared using two-way repeated measures ANOVA followed by the Tukey test. Agreement was assessed by Bland-Altman analysis. ENO values obtained with mouthpieces A and B were comparable for asthmatic (mean ± SEM, 42.9 ± 6.9 vs 43.3 ± 6.6 ppb) and non-asthmatic (13.3 ± 1.3 vs 13.7 ± 1.1 ppb) subjects. There was a significant difference in ENO between asthmatics and non-asthmatics using either mouthpiece A (P<0.001) or B (P<0.001). There was a positive correlation between mouthpiece A and mouthpiece B for both groups. The Bland-Altman limits of agreement were considered to be acceptable. Mouthpiece B was less expensive than A, and these data show that it can be used without compromising the result. Our data confirm reports of higher ENO values in the presence of airway inflammation.

Contrast sensitivity to angular frequency gratings is not higher than to Cartesian gratings

When contrast sensitivity functions to Cartesian and angular gratings were compared in previous studies the peak sensitivity to angular stimuli was reported to be 0.21 log units higher. In experiments carried out to repeat this result, we used the same two-alternative forced-choice paradigm, but improved experimental control and precision by increasing contrast resolution from 8 to 12 bits, increasing the screen refresh rate from 30 Hz interlaced to 85 Hz non-interlaced, linearizing the voltage-luminance relation, modulating luminance in frequencies that minimize pixel aliasing, and improving control of the subject's exposure to the stimuli. The contrast sensitivity functions to Cartesian and angular gratings were similar in form and peak sensitivity (2.4 cycles per visual degree (c/deg) and 32 c/360º, respectively) to those reported in a previous study (3 c/deg and 32 c/360º, respectively), but peak sensitivity to angular stimuli was 0.13 log units lower than that to Cartesian stimuli. When the experiment was repeated, this time simulating the experimental control level used in the previous study, no difference between the peak sensitivity to Cartesian and angular stimuli was found. This result agrees with most current models that assume Cartesian filtering at the first visual processing stage. The discrepancy in the results is explained in part by differences in the degree of experimental control.

Trabeculectomy and optic nerve head topography

The objective of the present study was to evaluate changes in optic nerve head parameters, measured by confocal laser tomography, before and after trabeculectomy in order to identify outcome measures for the management of glaucoma. The optic nerve head of 22 eyes (22 patients) was analyzed by confocal laser tomography with the Heidelberg retinal tomogram (HRT) before and after trabeculectomy. The median time between the first HRT and surgery was 4.6 months (mean: 7.7 ± 8.3) and the median time between surgery and the second HRT was 10.8 months (mean: 12.0 ± 6.8). The patients were divided into two groups, i.e., those with the highest (group A) and lowest (group B) intraocular pressure (IOP) change after surgery. Differences in the 12 standard topographic parameters before and after surgery for each group were evaluated by the Wilcoxon signed rank test and the differences in these parameters between the two groups were compared by the Mann-Whitney rank sum test. Multiple regression analysis was used to evaluate the influence of the change in IOP (deltaIOP and deltaIOP%) and the changes in the other parameters. There were significant differences in the HRT measures before and after surgery in group A only for cup volume. In group B, no parameter was statistically different. The changes in group A were not significantly different than those in group B for any parameter (P > 0.004, Bonferroni correction for multiple comparisons). deltaIOP and deltaIOP% had a statistically significant effect on delta cup disk area, delta cup volume and delta mean cup depth. Changes in cup shape size were influenced significantly only by deltaIOP. Some optic disc parameters measured by HRT presented a significant improvement after filtering surgery, depending on the amount of IOP reduction. Long-term studies are needed to determine the usefulness of these findings as outcome measures in the management of glaucoma.

Kalman filter for computational market dynamics

Kalman filter is a recursive mathematical power tool that plays an increasingly vital role in innumerable fields of study. The filter has been put to service in a multitude of studies involving both time series modelling and financial time series modelling. Modelling time series data in Computational Market Dynamics (CMD) can be accomplished using the Jablonska-Capasso-Morale (JCM) model. Maximum likelihood approach has always been utilised to estimate the parameters of the JCM model. The purpose of this study is to discover if the Kalman filter can be effectively utilized in CMD. Ensemble Kalman filter (EnKF), with 50 ensemble members, applied to US sugar prices spanning the period of January, 1960 to February, 2012 was employed for this work. The real data and Kalman filter trajectories showed no significant discrepancies, hence indicating satisfactory performance of the technique. Since only US sugar prices were utilized, it would be interesting to discover the nature of results if other data sets are employed.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Automatic recognition of fish from video sequences

The problem of automatic recognition of the fish from the video sequences is discussed in this Master’s Thesis. This is a very urgent issue for many organizations engaged in fish farming in Finland and Russia because the process of automation control and counting of individual species is turning point in the industry. The difficulties and the specific features of the problem have been identified in order to find a solution and propose some recommendations for the components of the automated fish recognition system. Methods such as background subtraction, Kalman filtering and Viola-Jones method were implemented during this work for detection, tracking and estimation of fish parameters. Both the results of the experiments and the choice of the appropriate methods strongly depend on the quality and the type of a video which is used as an input data. Practical experiments have demonstrated that not all methods can produce good results for real data, whereas on synthetic data they operate satisfactorily.

The effect of an aerobic training program on the electrical remodeling of the heart: high-frequency components of the signal-averaged electrocardiogram are predictors of the maximal aerobic power

Increased heart rate variability (HRV) and high-frequency content of the terminal region of the ventricular activation of signal-averaged ECG (SAECG) have been reported in athletes. The present study investigates HRV and SAECG parameters as predictors of maximal aerobic power (VO2max) in athletes. HRV, SAECG and VO2max were determined in 18 high-performance long-distance (25 ± 6 years; 17 males) runners 24 h after a training session. Clinical visits, ECG and VO2max determination were scheduled for all athletes during thew training period. A group of 18 untrained healthy volunteers matched for age, gender, and body surface area was included as controls. SAECG was acquired in the resting supine position for 15 min and processed to extract average RR interval (Mean-RR) and root mean squared standard deviation (RMSSD) of the difference of two consecutive normal RR intervals. SAECG variables analyzed in the vector magnitude with 40-250 Hz band-pass bi-directional filtering were: total and 40-µV terminal (LAS40) duration of ventricular activation, RMS voltage of total (RMST) and of the 40-ms terminal region of ventricular activation. Linear and multivariate stepwise logistic regressions oriented by inter-group comparisons were adjusted in significant variables in order to predict VO2max, with a P < 0.05 considered to be significant. VO2max correlated significantly (P < 0.05) with RMST (r = 0.77), Mean-RR (r = 0.62), RMSSD (r = 0.47), and LAS40 (r = -0.39). RMST was the independent predictor of VO2max. In athletes, HRV and high-frequency components of the SAECG correlate with VO2max and the high-frequency content of SAECG is an independent predictor of VO2max.

A novel polar-based human face recognition computational model

Motivated by a recently proposed biologically inspired face recognition approach, we investigated the relation between human behavior and a computational model based on Fourier-Bessel (FB) spatial patterns. We measured human recognition performance of FB filtered face images using an 8-alternative forced-choice method. Test stimuli were generated by converting the images from the spatial to the FB domain, filtering the resulting coefficients with a band-pass filter, and finally taking the inverse FB transformation of the filtered coefficients. The performance of the computational models was tested using a simulation of the psychophysical experiment. In the FB model, face images were first filtered by simulated V1- type neurons and later analyzed globally for their content of FB components. In general, there was a higher human contrast sensitivity to radially than to angularly filtered images, but both functions peaked at the 11.3-16 frequency interval. The FB-based model presented similar behavior with regard to peak position and relative sensitivity, but had a wider frequency band width and a narrower response range. The response pattern of two alternative models, based on local FB analysis and on raw luminance, strongly diverged from the human behavior patterns. These results suggest that human performance can be constrained by the type of information conveyed by polar patterns, and consequently that humans might use FB-like spatial patterns in face processing.