MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

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Molecular Systematics of Noctuoidea (Insecta, lepidoptera)

In this thesis, I conduct a series of molecular systematic studies on the large phytophagous moth superfamily Noctuoidea (Insecta, Lepidoptera) to clarify deep divergences and evolutionary affinities of the group, based on material from every zoogeographic region of the globe. Noctuoidea are the most speciose radiations of butterflies and moths on earth, comprising about a quarter of all lepidopteran diversity. The general aim of these studies was to apply suitably conservative genetic markers (DNA sequences of mitochondrial—mtDNA—and nuclear gene— nDNA—regions) to reconstruct, as the initial step, a robust skeleton phylogenetic hypothesis for the superfamily, then build up robust phylogenetic frameworks for those circumscribed monophyletic entities (i.e., families), as well as clarifying the internal classification of monophyletic lineages (subfamilies and tribes), to develop an understanding of the major lineages at various taxonomic levels within the superfamily Noctuoidea, and their inter-relationships. The approaches applied included: i) stabilizing a robust family-level classification for the superfamily; ii) resolving the phylogeny of the most speciose radiation of Noctuoidea: the family Erebidae; iii) reconstruction of ancestral feeding behaviors and evolution of the vampire moths (Erebidae, Calpinae); iv) elucidating the evolutionary relationships within the family Nolidae and v) clarifying the basal lineages of Noctuidae sensu stricto. Thus, in this thesis I present a wellresolved molecular phylogenetic hypothesis for higher taxa of Noctuoidea consisting of six strongly supported families: Oenosandridae, Notodontidae, Euteliidae, Erebidae, Nolidae, and Noctuidae. The studies in my thesis highlight the importance of molecular data in systematic and phylogenetic studies, in particular DNA sequences of nuclear genes, and an extensive sampling strategy to include representatives of all known major lineages of entire world fauna of Noctuoidea from every biogeographic region. This is crucial, especially when the model organism is as species-rich, highly diverse, cosmopolitan and heterogeneous as the Noctuoidea, traits that represent obstacles to the use of morphology at this taxonomic level.

Probabilistic position and orientation estimation of rigid objects using an RGB-D sensor

The recent emergence of low-cost RGB-D sensors has brought new opportunities for robotics by providing affordable devices that can provide synchronized images with both color and depth information. In this thesis, recent work on pose estimation utilizing RGBD sensors is reviewed. Also, a pose recognition system for rigid objects using RGB-D data is implemented. The implementation uses half-edge primitives extracted from the RGB-D images for pose estimation. The system is based on the probabilistic object representation framework by Detry et al., which utilizes Nonparametric Belief Propagation for pose inference. Experiments are performed on household objects to evaluate the performance and robustness of the system.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

The estimation of tuberculosis transmission parameters using ABC and MCMC methods

The aim of this work is to apply approximate Bayesian computation in combination with Marcov chain Monte Carlo methods in order to estimate the parameters of tuberculosis transmission. The methods are applied to San Francisco data and the results are compared with the outcomes of previous works. Moreover, a methodological idea with the aim to reduce computational time is also described. Despite the fact that this approach is proved to work in an appropriate way, further analysis is needed to understand and test its behaviour in different cases. Some related suggestions to its further enhancement are described in the corresponding chapter.

Semantic and fuzzy modelling for human behaviour recognition in smart spaces : a case study on ambient assisted living.

Human activity recognition in everyday environments is a critical, but challenging task in Ambient Intelligence applications to achieve proper Ambient Assisted Living, and key challenges still remain to be dealt with to realize robust methods. One of the major limitations of the Ambient Intelligence systems today is the lack of semantic models of those activities on the environment, so that the system can recognize the speci c activity being performed by the user(s) and act accordingly. In this context, this thesis addresses the general problem of knowledge representation in Smart Spaces. The main objective is to develop knowledge-based models, equipped with semantics to learn, infer and monitor human behaviours in Smart Spaces. Moreover, it is easy to recognize that some aspects of this problem have a high degree of uncertainty, and therefore, the developed models must be equipped with mechanisms to manage this type of information. A fuzzy ontology and a semantic hybrid system are presented to allow modelling and recognition of a set of complex real-life scenarios where vagueness and uncertainty are inherent to the human nature of the users that perform it. The handling of uncertain, incomplete and vague data (i.e., missing sensor readings and activity execution variations, since human behaviour is non-deterministic) is approached for the rst time through a fuzzy ontology validated on real-time settings within a hybrid data-driven and knowledgebased architecture. The semantics of activities, sub-activities and real-time object interaction are taken into consideration. The proposed framework consists of two main modules: the low-level sub-activity recognizer and the high-level activity recognizer. The rst module detects sub-activities (i.e., actions or basic activities) that take input data directly from a depth sensor (Kinect). The main contribution of this thesis tackles the second component of the hybrid system, which lays on top of the previous one, in a superior level of abstraction, and acquires the input data from the rst module's output, and executes ontological inference to provide users, activities and their in uence in the environment, with semantics. This component is thus knowledge-based, and a fuzzy ontology was designed to model the high-level activities. Since activity recognition requires context-awareness and the ability to discriminate among activities in di erent environments, the semantic framework allows for modelling common-sense knowledge in the form of a rule-based system that supports expressions close to natural language in the form of fuzzy linguistic labels. The framework advantages have been evaluated with a challenging and new public dataset, CAD-120, achieving an accuracy of 90.1% and 91.1% respectively for low and high-level activities. This entails an improvement over both, entirely data-driven approaches, and merely ontology-based approaches. As an added value, for the system to be su ciently simple and exible to be managed by non-expert users, and thus, facilitate the transfer of research to industry, a development framework composed by a programming toolbox, a hybrid crisp and fuzzy architecture, and graphical models to represent and con gure human behaviour in Smart Spaces, were developed in order to provide the framework with more usability in the nal application. As a result, human behaviour recognition can help assisting people with special needs such as in healthcare, independent elderly living, in remote rehabilitation monitoring, industrial process guideline control, and many other cases. This thesis shows use cases in these areas.

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.

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