In this work are discussed a block parameter estimation method for linear periodically time varying system. The whole work consists of two parts: theoretical and practical. The theoretical part is based on model’s description, its creation and structure. There it is shown estimation Markova, or an estimation of the least squares generalized method and the description of the generalized model. The practical part is devoted to fulfilling experiments and their describing. The conclusion about estimation of block parameter method’s achievement was also made. The experiments have been fulfilled using Matlab program. In addition count correctly Matlab (matrica, period) have been used. The results of experiments are given in the tables and schedules.

Neste trabalho são propostos métodos para a estimação de parâmetros de motores de indução através do método dos Mínimos Quadrados com medição apenas de tensões, correntes e resistência do estator em um ensaio de partida em vazio. São detalhados os procedimentos para o tratamento dos sinais medidos, além das estimações do fluxo magnético e da velocidade mecânica do motor. Para a estimação dos parâmetros elétricos, são propostos métodos que diferem nos requisitos e no tratamento dos parâmetros como invariantes ou variantes no tempo. Em relação a esse último caso, é empregado um método de estimação de parâmetros por janelas de dados, aplicando um modelo com parâmetros invariantes no tempo localmente em diversas partes do ensaio. São feitas simulações para validar os métodos propostos, e dados de ensaio de três motores de diferentes potências são utilizados para analisar a escala de variação paramétrica durante a partida. É feita uma comparação entre os resultados obtidos com e sem consideração de variação nos parâmetros. / In this work, methods are proposed to estimate the parameters of induction motors through the Least Squares method with the measurement of only voltages, currents and resistance of the stator in a no-load startup test. Procedures are detailed to process the measured signals, as well as to estimate magnetic flux and rotor mechanical speed. In order to estimate the electrical parameters, methods are proposed which differ in their requisites and in the treatment of parameters as time invariant or time-varying. For the latter, a methodology for parameter estimation through data windows is used, applying a model with time invariant parameters locally to different parts of the test. Simulations are made to validate the proposed methodology, and data from tests of three motors with different powers are used to analyze the scale of parameter variation during startup. A comparison is made between the results obtained with and without the consideration of variation in the parameters.

Neste trabalho são propostos métodos para a estimação de parâmetros de motores de indução através do método dos Mínimos Quadrados com medição apenas de tensões, correntes e resistência do estator em um ensaio de partida em vazio. São detalhados os procedimentos para o tratamento dos sinais medidos, além das estimações do fluxo magnético e da velocidade mecânica do motor. Para a estimação dos parâmetros elétricos, são propostos métodos que diferem nos requisitos e no tratamento dos parâmetros como invariantes ou variantes no tempo. Em relação a esse último caso, é empregado um método de estimação de parâmetros por janelas de dados, aplicando um modelo com parâmetros invariantes no tempo localmente em diversas partes do ensaio. São feitas simulações para validar os métodos propostos, e dados de ensaio de três motores de diferentes potências são utilizados para analisar a escala de variação paramétrica durante a partida. É feita uma comparação entre os resultados obtidos com e sem consideração de variação nos parâmetros. / In this work, methods are proposed to estimate the parameters of induction motors through the Least Squares method with the measurement of only voltages, currents and resistance of the stator in a no-load startup test. Procedures are detailed to process the measured signals, as well as to estimate magnetic flux and rotor mechanical speed. In order to estimate the electrical parameters, methods are proposed which differ in their requisites and in the treatment of parameters as time invariant or time-varying. For the latter, a methodology for parameter estimation through data windows is used, applying a model with time invariant parameters locally to different parts of the test. Simulations are made to validate the proposed methodology, and data from tests of three motors with different powers are used to analyze the scale of parameter variation during startup. A comparison is made between the results obtained with and without the consideration of variation in the parameters.

This thesis describes the design and implementation of genetic algorithm for approximation of non-linear mathematical functions using the least squares method. One objective of this work is to theoretically describe the basics of genetic algorithms. The second objective is to create a program that would be potentially used to approximate empirically measured data by the scientific institutions. Besides the theoretical description of the given subject, the text part of the work mainly deals with the design of the genetic algorithm and the whole application solving the given problem. Specific part of the assignment is that the developed application has to support approximation of points by various mathematical non-linear functions in several different intervals, and then it has to insure, that resulting functions are continuous throughout all the intervals. Described functionality is not offered by any available software.

Non-intrusive acoustic thermometry using an acoustic impulse generator and two microphones is developed and integrated with tomographic techniques to reconstruct temperature contours. A low velocity plume at around 450 °F exiting through a rectangular duct (3.25 by 10 inches) was used for validation and reconstruction. 0.3 % static temperature relative error compared with thermocouple-measured data was achieved using a cross-correlation algorithm to calculate speed of sound. Tomographic reconstruction algorithms, the simplified multiplicative algebraic reconstruction technique (SMART) and least squares method (LSQR), are investigated for visualizing temperature contours of the heated plume. A rectangular arrangement of transmitter and microphones with a traversing mechanism collected two orthogonal sets of acoustic projection data. Both reconstruction techniques have successfully recreated the overall characteristic of the contour; however, for the future work, the integration of the refraction effect and implementation of additional angled projections are required to improve local temperature estimation accuracy. The root-mean-square percentage errors of reconstructing non-uniform, asymmetric temperature contours using the SMART and LSQR method are calculated as 20% and 19%, respectively. / Master of Science

The diploma thesis deals with the self-tuning PSD controllers. The parameters of the model are obtained by a non-recurring method of least squares. With the assistance of the Matlab/Simulink programme, the individual processes of the PSD controller are compared on a second order system. In the thesis, a simulation of the self-tuning cascade control of PMSM‘s current and speed loop is created. The following part of the thesis covers the implementation of individual algorithms on the dSPACE platform for the real PMSM.

This paper focuses on the metamodel-based collaborative optimization (CO). The objective is to improve the computational efficiency of CO in order to handle multidisciplinary design optimization problems utilising high fidelity models. To address these issues, two levels of metamodel building techniques are proposed: metamodels in the disciplinary optimization are based on multi-fidelity modelling (the interaction of low and high fidelity models) and for the system level optimization a combination of a global metamodel based on the moving least squares method and trust region strategy is introduced. The proposed method is demonstrated on a continuous fiber-reinforced composite beam test problem. Results show that methods introduced in this paper provide an effective way of improving computational efficiency of CO based on high fidelity simulation models.

Thesis (PhD)--Stellenbosch University, 2008. / ENGLISH ABSTRACT: The growing need to improve accounting accuracy, precision and to standardise generally accepted measurement methods in the mining and processing industries has led to the joining of a number of organisations under the AMIRA International umbrella, with the purpose of fulfilling these objectives. As part of this venture, Anglo Platinum undertook a project on the material balancing around its largest smelter, the Waterval Smelter. The primary objective of the project was to perform a statistical material balance around the Waterval Smelter using the Maximum Likelihood method with respect to platinum, rhodium, nickel, sulphur and chrome (III) oxide. Pt, Rh and Ni were selected for their significant contribution to the company’s profit margin, whilst S was included because of its environmental importance. Cr2O3 was included for its importance in as far as the difficulties its presence poses in smelting of PGMs. The objective was achieved by performing a series of statistical computations. These include; quantification of total and analytical uncertainties, detection of outliers, estimation and modelling of daily and monthly measurement uncertainties, parameter estimation and data reconciliation. Comparisons were made between the Maximum Likelihood and Least Squares methods. Total uncertainties associated with the daily grades were determined by use of variographic studies. The estimated Pt standard deviations were within 10% relative to the respective average grades with a few exceptions. The total uncertainties were split into their respective components by determining analytical variances from analytical replicates. The results indicated that the sampling components of the total uncertainty were generally larger as compared to their analytical counterparts. WCM, the platinum rich Waterval smelter product, has an uncertainty that is worth ~R2 103 000 in its daily Pt grade. This estimated figure shows that the quality of measurements do not only affect the accuracy of metal accounting, but can have considerable implications if not quantified and managed. The daily uncertainties were estimated using Kriging and bootstrapped to obtain estimates for the monthly uncertainties. Distributions were fitted using MLE on the distribution fitting tool of the JMP6.0 programme and goodness of fit tests were performed. The data were fitted with normal and beta distributions, and there was a notable decrease in the skewness from the daily to the monthly data. The reconciliation of the data was performed using the Maximum Likelihood and comparing that with the widely used Least Squares. The Maximum Likelihood and Least Squares adjustments were performed on simulated data in order to conduct a test of accuracy and to determine the extent of error reduction after the reconciliation exercise. The test showed that the two methods had comparable accuracies and error reduction capabilities. However, it was shown that modelling of uncertainties with the unbounded normal distribution does lead to the estimation of adjustments so large that negative adjusted values are the result. The benefit of modelling the uncertainties with a bounded distribution, which is the beta distribution in this case, is that the possibility of obtaining negative adjusted values is annihilated. ML-adjusted values (beta) will always be non-negative, therefore feasible. In a further comparison of the ML(bounded model) and the LS methods in the material balancing of the Waterval smelter complex, it was found that for all those streams whose uncertainties were modelled with a beta distribution, i.e. those whose distribution possessed some degree of skewness, the ML adjustments were significantly smaller than the LS counterparts It is therefore concluded that the Maximum Likelihood (bounded models) is a rigorous alternative method of data reconciliation to the LS method with the benefits of; -- Better estimates due to the fact that the nature of the data (distribution) is not assumed, but determined through distribution fitting and parameter estimation -- Adjusted values can never be negative due to the bounded nature of the distribution The novel contributions made in this thesis are as follows; -- The Maximum Likelihood method was for the first time employed in the material balancing of non-normally distributed data and compared with the well-known Least Squares method -- This was an original integration of geostatistical methods with data reconciliation to quantify and predict measurement uncertainties. -- For the first time, measurement uncertainties were modeled with a distribution that was non-normal and bounded in nature, leading to smaller adjustments / AFRIKAANSE OPSOMMING: Die groeiende behoefte aan rekeningkundige akkuraatheid, en om presisie te verbeter, en te standardiseer op algemeen aanvaarde meetmetodes in die mynbou en prosesseringsnywerhede, het gelei tot die samwewerking van 'n aantal van organisasies onder die AMIRA International sambreel, met die doel om bogenoemde behoeftes aan te spreek. As deel van hierdie onderneming, het Anglo Platinum onderneem om 'n projek op die materiaal balansering rondom sy grootste smelter, die Waterval smelter. Die primêre doel van die projek was om 'n statistiese materiaal balans rondom die Waterval smelter uit te voer deur gebruik te maak van die sogenaamde maksimum waarskynlikheid metode met betrekking tot platinum, rodium, nikkel, swawel en chroom (iii) oxied. Pt, Rh en Ni was gekies vir hul beduidende bydrae tot die maatskappy se winsmarge, terwyl S ingesluit was weens sy belangrike omgewingsimpak. Cr2O3 was ingesluit weens sy impak op die smelting van Platinum groep minerale. Die doelstelling was bereik deur die uitvoering van 'n reeks van statistiese berekeninge. Hierdie sluit in: die kwantifisering van die totale en analitiese variansies, opsporing van uitskieters, beraming en modellering van daaglikse en maandelikse metingsvariansies, parameter beraming en data rekonsiliasie. Vergelykings was getref tussen die maksimum waarskynlikheid en kleinste kwadrate metodes. Totale onsekerhede of variansies geassosieer met die daaglikse grade was bepaal deur ’n Variografiese studie. Die beraamde Pt standaard afwykings was binne 10% relatief tot die onderskeie gemiddelde grade met sommige uitsonderings. Die totale onsekerhede was onderverdeel in hul onderskeie komponente deur bepaling van die ontledingsvariansies van duplikate. Die uitslae toon dat die monsternemings komponente van die totale onsekerheid oor die algemeen groter was as hul bypassende analitiese variansies. WCM, ‘n platinum-ryke Waterval Smelter produk, het 'n onsekerheid in die orde van ~twee miljoen rand in sy daagliks Pt graad. Hierdie beraamde waarde toon dat die kwaliteit van metings nie alleen die akkuraatheid van metaal rekeningkunde affekteer nie, maar aansienlike finansiële implikasies het indien nie die nie gekwantifiseer en bestuur word nie. Die daagliks onsekerhede was beraam deur gebruik te maak van “Kriging” en “Bootstrap” metodes om die maandelikse onsekerhede te beraam. Verspreidings was gepas deur gebruik te maak van hoogste waarskynlikheid beraming passings en goedheid–van-pas toetse was uitgevoer. Die data was gepas met Normaal en Beta verspreidings, en daar was 'n opmerklike vermindering in die skeefheid van die daaglikse tot die maandeliks data. Die rekonsiliasies van die massabalans data was uitgevoer deur die gebruik die maksimum waarskynlikheid metodes en vergelyk daardie met die algemeen gebruikde kleinste kwadrate metode. Die maksimum waarskynlikheid (ML) en kleinste kwadrate (LS) aanpassings was uitgevoer op gesimuleerde data ten einde die akkuraatheid te toets en om die mate van fout vermindering na die rekonsiliasie te bepaal. Die toets getoon dat die twee metodes het vergelykbare akkuraathede en foutverminderingsvermoëns. Dit was egter getoon dat modellering van die onsekerhede met die onbegrensde Normaal verdeling lei tot die beraming van aanpassings wat so groot is dat negatiewe verstelde waardes kan onstaan na rekosniliasie. Die voordeel om onsekerhede met 'n begrensde distribusie te modelleer, soos die beta distribusie in hierdie geval, is dat die moontlikheid om negatiewe verstelde waardes te verkry uitgelsuit word. ML-verstelde waardes (met die Beta distribusie funksie) sal altyd nie-negatief wees, en om hierdie rede uitvoerbaar. In 'n verdere vergelyking van die ML (begrensd) en die LS metodes in die materiaal balansering van die waterval smelter kompleks, is dit gevind dat vir almal daardie strome waarvan die onserkerhede gesimuleer was met 'n Beta distribusie, dus daardie strome waarvan die onsekerheidsdistribusie ‘n mate van skeefheid toon, die ML verstellings altyd beduidend kleiner was as die ooreenkomstige LS verstellings. Vervolgens word die Maksimum Waarskynlikheid metode (met begrensde modelle) gesien as 'n beter alternatiewe metode van data rekosiliasie in vergelyking met die kleinste kwadrate metode met die voordele van: • Beter beramings te danke aan die feit dat die aard van die onsekerheidsdistribusie nie aangeneem word nie, maar bepaal is deur die distribusie te pas en deur van parameter beraming gebruik te maak. • Die aangepaste waardes kan nooit negatief wees te danke aan die begrensde aard van die verdeling. Die volgende oorspronklike bydraes is gelewer in hierdie verhandeling: • Die Maksimum Waarskynlikheid metode was vir die eerste keer geëvalueer vir massa balans rekonsiliasie van nie-Normaal verspreide data en vergelyk met die bekendde kleinste kwadrate metode. • Dit is die eerste keer geostatistiese metodes geïntegreer is met data rekonsiliasie om onsekerhede te beraam waarbinne verstellings gemaak word. • Vir die eerste keer, is meetonsekerhede gemoddelleer met 'n distribusie wat nie- Normaal en begrensd van aard is, wat lei tot kleiner en meer realistiese verstellings.

The main purpose of this degree project is to reveal the Airbnb customer’s preferences and quantify the impact of non-market factors on the market price of tourist accommodation in Berlin, Germany. The data retrieved from Airbnb listings, publicly available on Inside Airbnb (2017), was supplemented on indicator of sharing economy accommodation using machine learning method in order to distinguish between amateur and business-running professional hosts. The main aim is to examine the consumers’ preferences and quantify the marginal effect of "real sharing economy" accommodation and other key variables on market price. This is accomplished by model approach using hedonic pricing method, which is used to estimate the economic value of particular attribute. Surprisingly, our data indicates the negative impact of sharing economy indicator on price. The set of motivations of consumers, which determine their valuation of Airbnb listings, was identified. The trade-off between encompass and parsimony of the set was desired in order to build an effective model. Calculation of proportion of explained variance showed that the price is affected mainly by number of accommodated persons, degree of privacy, number of bedrooms, cancellation policy, distance from the city centre and sharing economy indicator in decreasing order.

Simulation and modelling of turbulent flows under influence of streamline curvature and system rotation have been considered. Direct numerical simulations have been performed for fully developed rotating turbulent channel flow using a pseudo-spectral code. The rotation numbers considered are larger than unity. For the range of rotation numbers studied, an increase in rotation number has a damping effect on the turbulence. DNS-data obtained from previous simulations are used to perform a priori tests of different pressure-strain and dissipation rate models. Furthermore, the ideal behaviour of the coefficients of different model formulations is investigated. The main part of the modelling is focused on explicit algebraic Reynolds stress models (EARSMs). An EARSM based on a pressure strain rate model including terms that are tensorially nonlinear in the mean velocity gradients is proposed. The new model is tested for a number of flows including a high-lift aeronautics application. The linear extensions are demonstrated to have a significant effect on the predictions. Representation techniques for EARSMs based on incomplete sets of basis tensors are also considered. It is shown that a least-squares approach is favourable compared to the Galerkin method. The corresponding optimality aspects are considered and it is deduced that Galerkin based EARSMs are not optimal in a more strict sense. EARSMs derived with the least-squares method are, on the other hand, optimal in the sense that the error of the underlying implicit relation is minimized. It is further demonstrated that the predictions of the least-squares EARSMs are in significantly better agreement with the corresponding complete EARSMs when tested for fully developed rotating turbulent pipe flow. / QC 20100825