The calibration of model parameters is an important step in model development. Commonly, system output is measured, and model parameters are iteratively varied until the model output is a good match to the measured system output. Optimization algorithms are often used to identify the model parameter values. The presence of noise is difficult to avoid when physical processes are used to calibrate models due to measurement error, model structure error, and errors arising from numerical techniques and approximate solutions. Our study focuses on the effects of noise in parameter identification optimization problems. We generate six test problems, including five perturbations of a smooth problem. A previously studied groundwater parameter identification problem serves as our seventh test problem. We test the Nelder-Mead Algorithm, a combination of the Nelder-Mead Algorithm and Simulated Annealing, and the Shuffled Complex Evolution Method on these test problems. Comparison of optimization results for these problems reveals the effects of noise on optimization performance, including an increase in fitness values and a decrease in the number of fit evaluations. We vary the values of the internal algorithmic parameters to determine the effects of different values and present numerical results that indicate that changing the values of the algorithmic parameters can cause profound differences in optimization results for all three algorithms. A variation of the generally accepted parameter values for the Nelder-Mead Algorithm is recommended, and we determine that the Nelder-Mead/Simulated Annealing Hybrid and Shuffled Complex Evolution Method are too problem dependent for general recommendations for parameter values. Finally, we prove new convergence results for the Nelder-Mead/Simulated Annealing Hybrid in both smooth and noisy cases. / Ph. D.

The aim of this work is introduction with method of filtering the ECG signals using wavelet transformation and use of this method for filtering of signal disturbed with myopotencials. The work deals with general properties and with genesis of ECG signals and describes ECG curve. Next part of work is focused on wavelet transformation, types of wavelet transformation and different methods calculation thresholds and thresholding. Design part of work is focused on design Wiener filter for remove myopotencials from ECG signals and finding optimal parameters of this filter using optimization algorithm. For optimization is used simplex method. Discovered optimal parameters are assessed on CSE and MIT-BIH Arrhythmia database and compared with results of other authors.

Car following (CF) behaviour modelling has made significant progress in both traffic engi-neering and traffic psychology during recent decades. Autonomous vehicles (AVs) have been demonstrated to optimise traffic flow and increase traffic stability. Consequently, sever-al car-following models have been proposed based on various car following criteria, leading to a range of model parameter sets. In traffic engineering, Intelligent Driving Model (IDM) are commonly used as microscopic traffic flow models to simulate a single vehicle's behav-iour on a road. Observational data can be employed to parameter calibrate IDM models, which enhances their practicality for real-world applications. As a result, the calibration of model parameters is crucial in traffic simulation research and typically involves solving an optimization problem. Within the given context, the Nelder-Mead（NM）algorithm, particle swarm optimization (PSO) algorithm and genetic algorithm (GA) are utilized in this study for parameterizing the IDM model, using abundant trajectory data from five different road conditions. The study further examines the effects of various algorithms on the IDM model in different road sections, providing useful insights for traffic simulation and optimization.:Table of Contents CHAPTER 1 INTRODUCTION 1 1.1 BACKGROUND AND MOTIVATION 1 1.2 STRUCTURE OF THE WORK 3 CHAPTER 2 BACKGROUND AND RELATED WORK 4 2.1 CAR-FOLLOWING MODELS 4 2.1.1 General Motors model and Gazis-Herman-Rothery model 5 2.1.2 Optimal velocity model and extended models 6 2.1.3 Safety distance or collision avoidance models 7 2.1.4 Physiology-psychology models 8 2.1.5 Intelligent Driver model 10 2.2 CALIBRATION OF CAR-FOLLOWING MODEL 12 2.2.1 Statistical Methods 13 2.2.2 Optimization Algorithms 14 2.3 TRAJECTORY DATA 21 2.3.1 Requirements of Experimental Data 22 2.3.2 Data Collection Techniques 22 2.3.3 Collected Experimental Data 24 CHAPTER 3 EXPERIMENTS AND RESULTS 28 3.1 CALIBRATION PROCESS 28 3.1.1 Objective Function 29 3.1.2 Errors Analysis 30 3.2 SOFTWARE AND METHODOLOGY 30 3.3 NM RESULTS 30 3.4 PSO RESULTS 37 3.4.1 PSO Calibrator 37 3.4.2 PSO Results 44 3.5 GA RESULTS 51 3.6 OPTIMIZATION PERFORMANCE ANALYSIS 58 CHAPTER 4 CONCLUSION 60 REFERENCES 62

This master´s thesis deals with the registration of ultrasound sequences using evolutionary algorithms. The theoretical part of the thesis describes the process of image registration and its optimalization using genetic and metaheuristic algorithms. The thesis also presents problems that may occur during the registration of ultrasonographic images and various approaches to their registration. In the practical part of the work, several optimization methods for the registration of a number of sequences were implemented and compared.

This thesis proposes a new class of bivariate autoregressive conditional median duration models for matched high-frequency data and develops some inferential methods for an existing univariate model as well as the bivariate models introduced here to facilitate model fitting and forecasting. During the last two decades, the autoregressive conditional mean duration (ACD) model has been playing a dominant role in analyzing irregularly spaced high-frequency financial data. Univariate ACD models have been extensively discussed in the literature. However, some major challenges remain. The existing ACD models do not provide a good distributional fit to financial durations, which are right-skewed and often exhibit unimodal hazard rates. Birnbaum-Saunders (BS) distribution is capable of modeling a wide variety of positively skewed data. Median is not only a robust measure of central tendency, but also a natural scale parameter of the BS distribution. A class of conditional median duration models, the BS-ACD and the scale-mixture BS ACD models based on the BS, BS power-exponential and Student-t BS (BSt) distributions, have been suggested in the literature to improve the quality of the model fit. The BSt-ACD model is more flexible than the BS-ACD model in terms of kurtosis and skewness. In Chapter 2, we develop the maximum likelihood estimation method for the BSt-ACD model. The estimation is performed by utilizing a hybrid of optimization algorithms. The performance of the estimates is then examined through an extensive Monte Carlo simulation study. We also carry out model discrimination using both likelihood-based method and information-based criterion. Applications to real trade durations and comparison with existing alternatives are then made. The bivariate version of the ACD model has not received attention due to non-synchronicity. Although some bivariate generalizations of the ACD model have been introduced, they do not possess enough flexibility in modeling durations since they are conditional mean-based and do not account for non-monotonic hazard rates. Recently, the bivariate BS (BVBS) distribution has been developed with many desirable properties and characteristics. It allows for unimodal shapes of marginal hazard functions. In Chapter 3, upon using this bivariate BS distribution, we propose the BVBS-ACD model as a natural bivariate extension of the BS-ACD model. It enables us to jointly analyze matched duration series, and also capture the dependence between the two series. The maximum likelihood estimation of the model parameters and associated inferential methods have been developed. A Monte Carlo simulation study is then carried out to examine the performance of the proposed inferential methods. The goodness-of-fit and predictive performance of the model are also discussed. A real bivariate duration data analysis is provided to illustrate the developed methodology. The bivariate Student-t BS (BVBSt) distribution has been introduced in the literature as a robust extension of the BVBS distribution. It provides greater flexibility in terms of the kurtosis and skewness through the inclusion of an additional shape parameter. In Chapter 4, we propose the BVBSt-ACD model as a natural extension of the BSt-ACD model to the bivariate case. We then discuss the maximum likelihood estimation of the model parameters. A simulation study is carried out to investigate the performance of these estimators. Model discrimination is then done by using information-based criterion. Methods for evaluating the goodness-of-fit and predictive ability of the model are also discussed. A simulated data example is used to illustrate the proposed model as compared to the BVBS-ACD model. Finally, in Chapter 5, some concluding comments are made and also some problems for future research are mentioned. / Thesis / Master of Science (MSc)