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.

Automatic meter reading – benefits and applications

In liberalized electricity markets, which have taken place in many countries over the world, the electricity distribution companies operate in the competitive conditions. Therefore, accurate information about the customers’ energy consumption plays an essential role for the budget keeping of the distribution company and for correct planning and operation of the distribution network. This master’s thesis is focused on the description of the possible benefits for the electric utilities and residential customers from the automatic meter reading system usage. Major benefits of the AMR, illustrated in the thesis, are distribution network management, power quality monitoring, load modelling, and detection of the illegal usage of the electricity. By the example of the power system state estimation, it was illustrated that even the partial installation of the AMR in the customer side leads to more accurate data about the voltage and power levels in the whole network. The thesis also contains the description of the present situation of the AMR integration in Russia.

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

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.

Calculation of the critical crack size for cold form rectangular hollow section tube (CRHS) under bending load at -40º C temperature

To predict the capacity of the structure or the point which is followed by instability, calculation of the critical crack size is important. Structures usually contain several cracks but not necessarily all of these cracks lead to failure or reach the critical size. So, defining the harmful cracks or the crack size which is the most leading one to failure provides criteria for structure’s capacity at elevated temperature. The scope of this thesis was to calculate fracture parameters like stress intensity factor, the J integral and plastic and ultimate capacity of the structure to estimate critical crack size for this specific structure. Several three dimensional (3D) simulations using finite element method by Ansys program and boundary element method by Frank 3D program were carried out to calculate fracture parameters and results with the aid of laboratory tests (loaddisplacement curve, the J resistance curve and yield or ultimate stress) leaded to extract critical size of the crack. Two types of the fracture which is usually affected by temperature, Elastic and Elasti-Plastic fractures were simulated by performing several linear elastic and nonlinear elastic analyses. Geometry details of the weldment; flank angle and toe radius were also studied independently to estimate the location of crack initiation and simulate stress field in early stages of crack extension in structure. In this work also overview of the structure’s capacity in room temperature (20 ºC) was studied. Comparison of the results in different temperature (20 ºC and -40 ºC) provides a threshold of the structure’s behavior within the defined range.

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.

Mobile system for pump working point estimation

In the current economy situation companies try to reduce their expenses. One of the solutions is to improve the energy efficiency of the processes. It is known that the energy consumption of pumping applications range from 20 up to 50% of the energy usage in the certain industrial plants operations. Some studies have shown that 30% to 50% of energy consumed by pump systems could be saved by changing the pump or the flow control method. The aim of this thesis is to create a mobile measurement system that can calculate a working point position of a pump drive. This information can be used to determine the efficiency of the pump drive operation and to develop a solution to bring pump’s efficiency to a maximum possible value. This can allow a great reduction in the pump drive’s life cycle cost. In the first part of the thesis, a brief introduction in the details of pump drive operation is given. Methods that can be used in the project are presented. Later, the review of available platforms for the project implementation is given. In the second part of the thesis, components of the project are presented. Detailed description for each created component is given. Finally, results of laboratory tests are presented. Acquired results are compared and analyzed. In addition, the operation of created system is analyzed and suggestions for the future development are given.

Estimation of existing cable systems in generator-busbar unit and choice the optimal solution for its modernization

The aim of this master’s thesis is to develop an algorithm to calculate the cable network for heat and power station CHGRES. This algorithm includes important aspect which has an influence on the cable network reliability. Moreover, according to developed algorithm, the optimal solution for modernization cable system from economical and technical point of view was obtained. The conditions of existing cable lines show that replacement is necessary. Otherwise, the fault situation would happen. In this case company would loss not only money but also its prestige. As a solution, XLPE single core cables are more profitable than other types of cable considered in this work. Moreover, it is presented the dependence of value of short circuit current on number of 10/110 kV transformers connected in parallel between main grid and considered 10 kV busbar and how it affects on final decision. Furthermore, the losses of company in power (capacity) market due to fault situation are presented. These losses are commensurable with investment to replace existing cable system.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Kernel-Based Ranking. Methods for Learning and Performance Estimation

Machine learning provides tools for automated construction of predictive models in data intensive areas of engineering and science. The family of regularized kernel methods have in the recent years become one of the mainstream approaches to machine learning, due to a number of advantages the methods share. The approach provides theoretically well-founded solutions to the problems of under- and overfitting, allows learning from structured data, and has been empirically demonstrated to yield high predictive performance on a wide range of application domains. Historically, the problems of classification and regression have gained the majority of attention in the field. In this thesis we focus on another type of learning problem, that of learning to rank. In learning to rank, the aim is from a set of past observations to learn a ranking function that can order new objects according to how well they match some underlying criterion of goodness. As an important special case of the setting, we can recover the bipartite ranking problem, corresponding to maximizing the area under the ROC curve (AUC) in binary classification. Ranking applications appear in a large variety of settings, examples encountered in this thesis include document retrieval in web search, recommender systems, information extraction and automated parsing of natural language. We consider the pairwise approach to learning to rank, where ranking models are learned by minimizing the expected probability of ranking any two randomly drawn test examples incorrectly. The development of computationally efficient kernel methods, based on this approach, has in the past proven to be challenging. Moreover, it is not clear what techniques for estimating the predictive performance of learned models are the most reliable in the ranking setting, and how the techniques can be implemented efficiently. The contributions of this thesis are as follows. First, we develop RankRLS, a computationally efficient kernel method for learning to rank, that is based on minimizing a regularized pairwise least-squares loss. In addition to training methods, we introduce a variety of algorithms for tasks such as model selection, multi-output learning, and cross-validation, based on computational shortcuts from matrix algebra. Second, we improve the fastest known training method for the linear version of the RankSVM algorithm, which is one of the most well established methods for learning to rank. Third, we study the combination of the empirical kernel map and reduced set approximation, which allows the large-scale training of kernel machines using linear solvers, and propose computationally efficient solutions to cross-validation when using the approach. Next, we explore the problem of reliable cross-validation when using AUC as a performance criterion, through an extensive simulation study. We demonstrate that the proposed leave-pair-out cross-validation approach leads to more reliable performance estimation than commonly used alternative approaches. Finally, we present a case study on applying machine learning to information extraction from biomedical literature, which combines several of the approaches considered in the thesis. The thesis is divided into two parts. Part I provides the background for the research work and summarizes the most central results, Part II consists of the five original research articles that are the main contribution of this thesis.