This thesis considers the practical problem of constrained and unconstrained local optimization. This subject has been well studied when the objective function f is assumed to smooth. However, nonsmooth problems occur naturally and frequently in practice. Here f is assumed to be nonsmooth or discontinuous without forcing smoothness assumptions near, or at, a potential solution. Various methods have been presented by others to solve nonsmooth optimization problems, however only partial convergence results are possible for these methods. In this thesis, an optimization method which use a series of local and localized global optimization phases is proposed. The local phase searches for a local minimum and gives the methods numerical performance on parts of f which are smooth. The localized global phase exhaustively searches for points of descent in a neighborhood of cluster points. It is the localized global phase which provides strong theoretical convergence results on nonsmooth problems. Algorithms are presented for solving bound constrained, unconstrained and constrained nonlinear nonsmooth optimization problems. These algorithms use direct search methods in the local phase as they can be applied directly to nonsmooth problems because gradients are not explicitly required. The localized global optimization phase uses a new partitioning random search algorithm to direct random sampling into promising subsets of ℝⁿ. The partition is formed using classification and regression trees (CART) from statistical pattern recognition. The CART partition defines desirable subsets where f is relatively low, based on previous sampling, from which further samples are drawn directly. For each algorithm, convergence to an essential local minimizer of f is demonstrated under mild conditions. That is, a point x* for which the set of all feasible points with lower f values has Lebesgue measure zero for all sufficiently small neighborhoods of x*. Stopping rules are derived for each algorithm giving practical convergence to estimates of essential local minimizers. Numerical results are presented on a range of nonsmooth test problems for 2 to 10 dimensions showing the methods are effective in practice.

In this thesis we propose four new methods for solving constrained global optimization problems. The first proposed algorithm is a differential evolution (DE) algorithm using penalty functions for constraint handling. The second algorithm is based on the first DE algorithm but also incorporates a filter set as a diversification mechanism. The third algorithm is also based on DE but includes an additional local refinement process in the form of the pattern search (PS) technique. The last algorithm incorporates both the filter set and PS into the DE algorithm for constrained global optimization. The superiority of feasible points (SFP) and the parameter free penalty (PFP) schemes are used as constraint handling mechanisms. The new algorithms were numerically tested using two sets of test problems and the results where compared with those of the genetic algorithm (GA). The comparison shows that the new algorithms outperformed GA. When the new methods are compared to each other, the last three methods performed better than the first method i.e. the DE algorithm. The new algorithms show promising results with potential for further research. Keywords: constrained global optimization, differential evolution, pattern search, filter method, penalty function, superiority of feasible points, parameter free penalty. ii

<div>The objective of this doctoral research was to develop a versatile inverse heat transfer approach, that would enable the solution of small scale problems present in microelectronics, as well as the analysis of the complex heat flux in turbines. An inverse method is a mathematical approach which allows the resolution of problems starting from the solution. In a direct problem, the boundary conditions are given, and using the governing physics principles and equations you can calculate the solution or physical effect. In an inverse method, the solution is provided and through the physical equations, the boundary conditions can be determined. Therefore, the inverse method applied to heat transfer means that we know the variation of temperature (effect) over time and space. With the temperature input, the geometry, thermal properties of the test article and the heat diffusion equation, we can compute the spatially- and temporally-varying heat flux that generated the temperature map.</div><div><br></div><div>This doctoral dissertation develops two inverse methodologies: (1) an optimization methodology based on the conjugate gradient method and (2) a function specification method combined with a regularization technique, which is less robust but much faster. We implement these methodologies with commercial codes for solving conductive heat transfer with COMSOL and for conjugate heat transfer with ANSYS Fluent.</div><div><br></div><div>The goal is not only the development of the methods but also the validation of the techniques in two different fields with a common purpose: quantifying heat dissipation. The inverse methods were applied in the micro-scale to the dissipation of heat in microelectronics and in the macro-scale to the gas turbine engines.<br></div><div><br></div><div>In microelectronics, we performed numerical and experimental studies of the two developed inverse methodologies. The intent was to predict where heat is being dissipated and localized hot spots inside of the chip from limited measurements of the temperature outside of the chip. Here, infrared thermography of the chip surface is the input to the inverse methods leveraging thermal model of the chip. Furthermore, we combined the inverse methodology with a Kriging interpolation technique with genetic algorithm optimization to optimize the location and number of the temperature sensors inside of the chip required to accurately predict the thermal behavior of the microchip at each moment of time and everywhere.<br></div><div><br></div><div>In the application for gas turbine engines, the inverse method can be useful to detect or predict the conditions inside of the turbine by taking measurements in the outer casing. Therefore, the objective is the experimental validation of the technique in a wind tunnel especially designed with optical access for non-contact measurement techniques. We measured the temperature of the outer casing of the turbine rotor with an infrared camera and surface temperature sensors and this information is the input of the two methodologies developed in order to predict which the heat flux through the turbine casing. A new facility, specifically, an annular turbine cascade, was designed to be able to measure the relative frame of the rotor from the absolute frame. In order to get valuable data of the heat flux in a real engine, we need to replicate the Mach, Reynolds, and temperature ratios between fluid and solid. Therefore, the facility can reproduce a large range of pressures and flow temperatures. Because some regions of interest are not accessible, this researchprovides a significant benefit for understanding the system performance from limited data. With inverse methods, we can measure the outside of objects and provide an accurate prediction of the behavior of the complete system. This information is relevant not only for new designs of gas turbines or microchips, but also for old designs where due to lack of prevision there are not enough sensors to monitor the thermal behavior of the studied system.<br></div><div><br></div>

The thesis introduces an overview of techniques for filtering of unobserved variables using a state-space representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter, its extension into a form of a non-linear filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semi-structural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed non-negative state constraint on the interest rate. Results of the algorithms are compared and discussed.

Passenger ride vibration comfort is a critical aspect to consider while developing any vehicle and there is a need to understand how the occupants would be affected when driving on different road profile roughness. Hence, road profile generation is critical as road profiles are used as inputs to simulation tools to investigate vehicle dynamic behaviour in depth. At the same time, the optimisation of the vehicle characteristics can be conducted on the various road profiles in order to identify a solution that can provide enhanced ride comfort and improve vehicle handling for all the investigated road profiles. The objective of this thesis is to study ride vibrational comfort and optimise the suspension system for theNational Electric Vehicle Sweden (NEVS) vehicle model for better ride comfort and road holding. Synthetic road profiles are generated by using stochastic processes according to International Organization for Standardization (ISO) 8608 standards. Further, simulations are conducted in MSC ADAMS Car software using the generated synthetic road profiles for a rigid body NEVS vehicle model to study the vertical accelerations. The analysis includes the investigations of the acceleration Power Spectral Density (PSD) and observations are made on the peaks that appear (at Front Seat Rail (FSR) which is the sprung mass of the vehicle and Wheel centre (WC) which is the un-sprung mass of the vehicle) for different road types and vehicle velocities. It is decided that the comfort objective will be used considering the weighted Root Mean Square (RMS) accelerations. Further, the suspension system of the vehicle model is optimised for three different road profiles (A, B, and C) based on the objectives of ride comfort and handling using a suitable vehicle model with the same characteristics as theNEVScar. A multi-objective optimisation technique is used and the optimised results are observed and discussed. Optimal objectives (based on a compromise between ride comfort and road holding) for the suspension system are determined for each investigated road profile. / Vibrationskomfort för passagerare är en kritisk aspekt att tänka på när man utvecklar ett fordon och det finns ett behov av att förstå hur passagerarna kan påverkas när de åker på olika vägprofiler. Därför är vägprofilgenerering avgörande eftersom vägprofiler används som input till simuleringsverktyg för att undersöka fordonets dynamiska beteende. Samtidigt kan optimeringen av fordonets egenskaper utföras på de olika vägprofilerna för att identifiera en lösning som kan ge ökad åkkomfort och förbättra fordonshanteringen för alla undersökta vägprofiler. Syftet med detta examensarbete är att studera körvibrationskomfort och optimera fjädringssystemet för NEVS fordonsmodellen för bättre åkkomfort och väghållning. Syntetiska vägprofiler genereras genom att använda stokastiska processer enligt ISO 8608 standarder. Dessutom utförs simuleringar i MSC ADAMS programvara med hjälp av de genererade syntetiska vägprofilerna för en stelkropps NEVS fordonsmodell för att studera de vertikala accelerationerna. Analysen inkluderar undersökningar av accelerations PSD och observationer görs av topparna som visas (vid FSR och WC) för olika vägtyper och fordonshastigheter. Det beslutas att komfortmålet kommer att utvärderas med hänsyn till endast de vägda RMS accelerationerna. Dessutom är fordonsmodellens hjul upphängningssystem optimerat för tre olika vägprofiler (A, B och C) baserat på målen för åkkomfort och väghållning med hjälp av en lämplig fordonsmodell med samma egenskaper som NEVS bilen. En multi-purpose optimeringsteknik används och de optimerade resultaten observeras och diskuteras. Optimala mål (baserat på en kompromiss mellan åkkomfort och väghållning) för fjädringssystemet bestäms för varje undersökt vägprofil.

Made available in DSpace on 2016-12-12T20:27:37Z (GMT). No. of bitstreams: 1 Yujuan Wang.pdf: 1608760 bytes, checksum: 9cb82304a2c95c2b0e357dc7f8449815 (MD5) Previous issue date: 2012-12-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents the development of an FPGA-based optical interrogation system of multiplexed FBG sensors. The Fabry-Perot filter is used to implement the tunable filter method, as a demodulator for FBG sensors. The tuning signal generation for Fabry-Perot filter and the data aquisition are implemented and syncronized em FPGA. Peak-detection algorithms, based on centroid and FIR filter, are implemented em FPGA. The peak displacement detected of FBG reflected spectrum is used to refer sensed elements, such as variation of temperature and refractive index. Besides, other auxiliary digital circuits are implemented for the system configuration, visulization of the detected peak information and the serial communication to monitor entire spectra in computer. All these digital circuits are working on their own duty at the same time, synchronised by the crystal clock of FPGA. The system was used to monitor the fabrication process of an refractive index sensor. The fabricated sensor was tested by measuring the refractive index of water and sucrose. In another experiment, the system was tested by measuring the temperature of a water sample. In addition, a method to calibrate the tuning signal generator is proposed, which can also be employed in other applications that uses DA converters. Finally, the developed system was packaged to facilitate its transportation. / Este trabalho descreve a implementação de um sistema de interrogação óptico para FBGs multiplexadas, com o controle dos processos implementado em FPGA. A interrogação das FBGs é realizada por meio do método de filtro sintonizável, com o uso de filtro Fabry-Perot. Um FPGA é utilizado para gerar sinal de sintonia para o filtro Fabry-Perot e realizar a leitura do sinal espectral refletido pelas FBGs. Algoritmos de detecção de pico (centroide e filtro FIR) foram implementados no FPGA para processar os sinais refletidos por cada FBG, com o objetivo de inferir as propriedades sensoreadas, como variação de temperatura ou índice de refração. Além destes circuitos digitais, são implementados outros circuitos digitais para a configuração do sistema, para a visualização do pico detectado do sinal espectral e para o monitoramento do espectro inteiro via comunicação serial. Todos circuitos cumprem a própria função paralelamente em virtude do paralelismo do FPGA, sincronizado pelo clock do oscilador cristal do FPGA. O sistema desenvolvido foi utilizado no monitoramento do processo de fabricação de sensor de índice de refração e então na leitura do índice de refração de amostras de sacarose e água. O sistema também foi utilizado para a leitura da temperatura de amostras de água, onde foi estimada a sensibilidade e a resolução do sistema. Também foi proposto um método para a calibração do sistema, que pode ser utilizado também em outros trabalhos. O sistema final foi colocado em uma maleta para facilitar o seu transporte para o local de uso.