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.

Statistical segmentation methods and color variance analysis of retinal images

In this research, the effectiveness of Naive Bayes and Gaussian Mixture Models classifiers on segmenting exudates in retinal images is studied and the results are evaluated with metrics commonly used in medical imaging. Also, a color variation analysis of retinal images is carried out to find how effectively can retinal images be segmented using only the color information of the pixels.

Kylmälaitekoneikon runkorakenteen kehittäminen

Kylmälaitekoneikot ovat kylmäkomponentteja sisältäviä rakenteita, joiden avulla toteutetaan suurten tilojen, kuten elintarvikemyymälöiden sisäilman jäähdytys. Lisäksi koneikkojen avulla jäähdytetään matalampiin lämpötiloihin pienempiä kylmähuoneita. Osa koneikoista ottaa talteen kylmäprosessissa syntyvän lämmön, jota hyödynnetään tilojen lämmityksessä. Tämän diplomityön tavoitteena oli suunnitella ja mitoittaa kahdeksalle eri kylmälaitekoneikolle entistä kustannustehokkaammat runkorakenteet, jotka ovat niin kestäviä, että koneikkoja on mahdollista pinota tilan säästämiseksi kolme päällekkäin. Lisäksi runkorakenteilta vaadittiin helppoa kuljetettavuutta, hyviä kiinnitysominaisuuksia ja korroosionkestävyyttä. Aluksi työssä selvitettiin runkorakenteisiin kohdistuvat vaatimukset, jonka jälkeen materiaalin valinta tehtiin materiaaliin kohdistuvien vaatimusten perusteella. Rakenteiden palkit mitoitettiin tarvittavan taivutusvastuksen ja kiepahduksen mukaan. Pilarit puolestaan mitoitettiin nurjahduksen ja kaksiaksiaalisen taivutustilan perusteella. Tämän jälkeen mitoitettiin eri sauvojen väliset hitsi- ja ruuviliitokset siten, että rakenne hajoaa ylikuormitustilanteessa mahdollisimman turvallisesti. Työssä tehdyt laskelmat varmennettiin elementtimenetelmän avulla ja lopullisille rakenteille tehtiin elementtimenetelmällä vielä ominaistaajuusanalyysejä. Lopuksi työssä suunniteltiin runkorakenteille sopiva korroosionsuojaus.

Generative Part-Based Gabor Object Detector

Object detection is a fundamental task of computer vision that is utilized as a core part in a number of industrial and scientific applications, for example, in robotics, where objects need to be correctly detected and localized prior to being grasped and manipulated. Existing object detectors vary in (i) the amount of supervision they need for training, (ii) the type of a learning method adopted (generative or discriminative) and (iii) the amount of spatial information used in the object model (model-free, using no spatial information in the object model, or model-based, with the explicit spatial model of an object). Although some existing methods report good performance in the detection of certain objects, the results tend to be application specific and no universal method has been found that clearly outperforms all others in all areas. This work proposes a novel generative part-based object detector. The generative learning procedure of the developed method allows learning from positive examples only. The detector is based on finding semantically meaningful parts of the object (i.e. a part detector) that can provide additional information to object location, for example, pose. The object class model, i.e. the appearance of the object parts and their spatial variance, constellation, is explicitly modelled in a fully probabilistic manner. The appearance is based on bio-inspired complex-valued Gabor features that are transformed to part probabilities by an unsupervised Gaussian Mixture Model (GMM). The proposed novel randomized GMM enables learning from only a few training examples. The probabilistic spatial model of the part configurations is constructed with a mixture of 2D Gaussians. The appearance of the parts of the object is learned in an object canonical space that removes geometric variations from the part appearance model. Robustness to pose variations is achieved by object pose quantization, which is more efficient than previously used scale and orientation shifts in the Gabor feature space. Performance of the resulting generative object detector is characterized by high recall with low precision, i.e. the generative detector produces large number of false positive detections. Thus a discriminative classifier is used to prune false positive candidate detections produced by the generative detector improving its precision while keeping high recall. Using only a small number of positive examples, the developed object detector performs comparably to state-of-the-art discriminative methods.

Convenience of scallops in plate structures

In this thesis was performed comprehensive study about the convenience of scallops in plate structures. A literature review was performed and lack of knowledge was fulfilled with fatigue tests performed in the laboratory of Steel Structures at the Lappeenranta University of Technology and with finite element method. The aim of this thesis was to produce design guidance for the use of scallops for different structural details and different loading conditions. An additional aim was to include more precise instructions for scallop design to produce good fatigue resistance and appropriate manufacturing quality. The literature review was performed searching bridge engineering and maritime standards and design guides and studies from scientific databases and reference lists from the literature of this field. Fatigue tests were used to research the effect of using scallops or not using scallops to fatigue strength of bracket specimen. Tests were performed on three specimens with different scallop radii and to five specimens without scallops with different weld penetration depths. Finite element method using solid elements, symmetry and submodels was used to determine stress concentration factors for I-beams with scallops. Stresses were defined with hot spot stress method. Choosing to use a scallop or not in the structure is affected by many factors, such as structural and loading conditions and manufacturability. As a rule of thumb, scallops should be avoided because those cause stress concentration points to the structure and take a lot of time to manufacture. When scallops are not used, good quality welding should be provided and full weld penetration is recommended to be used in load carrying corner weld areas. In some cases, it is advisable to use scallops. In that case, circular scallops are recommended to be used and radius should be chosen from fatigue strength or manufacturing point of view.

Robotiikkatuoteperheen kehittäminen

Robottiikkatuoteperheeseen kuuluu robottihitsausportaalit, joiden päärunko rakentuu kote-lopalkeista. Koteloprofiilien käyttö on suosittua teollisuuden eri aloilla ja se soveltuu hyvin raskaaseen konepajateollisuuteen. Hitsausrobottiportaalin suunnitteluun liittyy monia eri vaiheita ja valituilla teknisillä ratkaisuilla voidaan vaikuttaa valmistettavan tuotteen hitsin laatuun ja työn onnistumiseen. Hitsausrobottiportaalit ovat usein asiakasräätälöityjä ratkaisuja, jolloin suunnittelutyö sekä valmistusvaihe vaativat runsaasti kapasiteettia. Modulaarisuuden avulla suunnittelu- ja valmistusvaiheita on mahdollista nopeuttaa sekä parantaa tuotteen testausta, huollettavuutta ja laatua. Tässä diplomityössä tutkittiin, miten hitsausrobottiportaalin vaakapuomi käyttäytyy ja taipuu erilaisissa kuormitustilanteissa. Lisäksi työssä määritettiin alkuperäisen koteloprofiilin tilalle uusi optimoitu koteloprofiili sekä tarkasteltiin moduloinnin mahdollistamista robo-tiikkatuoteperheen portaalisovelluksiin.