In this paper we deal with aspects of characterizing the ill-posedn ess of nonlinear inverse problems based on the discussion of specific examples. In particular, a parameter identification problem to a second order differential equation and its ill-posed linear components are under consideration. A new approach to the classification ofill-posedness degrees for multiplication operators completes the paper.

Made available in DSpace on 2016-12-08T17:19:33Z (GMT). No. of bitstreams: 1 Capa.pdf: 100296 bytes, checksum: 85da33d7d5aa32b41734416b7ba82f1a (MD5) Previous issue date: 2009-09-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Numerical simulation of metal forming processes requires a constitutive model, which depends upon adequate material parameters. A direct determination of material parameters usually admits homogeneous stress and strain states in the specimen, thereby narrowing the application range to moderate deformations or even compromising accuracy in some industrial applications. Therefore, a combined experimental and numerical technique based on optimisation strategies is recommended. Such method is generally known as parameter identification and produces stress states close to those to be verified in industrial operations. In this work, a parameter identification technique based upon deep drawing experiments is presented. Sensitivity analysis is performed using a modified finite difference method, and the optimization itself is developed using quadratic programming. Sensitivity results using the classical and the modified finite difference methods are studied and compared, especially with respect to the application of automatic or imposed step increments. It is observed that the modified method yields a more effective behaviour with respect to the automatic time step strategy, allowing use of a wider range of penalization factors and attaining greater efficiency. Several identification problems are presented showing qualitative agreement with related research in the literature. Difficulties arise in the simultaneous determination of multiple material parameters, due to typical flat regions or to the presence of local minima in the design space, suggesting future combination of the presented approach with evolutionary algorithms. / Toda simulação numérica de um processo de conformação mecânica requer um modelo constitutivo, que depende de parâmetros materiais adequados. Muitas vezes a determinação direta dos parâmetros materiais admite um estado homogêneo de tensão e deformação no corpo de prova, provocando um estreitamento na sua faixa de aplicação as situações onde ocorrem deformações moderadas ou então comprometendo a precisão dos resultados em algumas aplicações industriais. Portanto, uma combinação entre as técnicas numérica e experimental utilizando técnicas de otimização é recomendada. Esta estratégia é geralmente conhecida como identificação de parâmetros e produz estados de tensão próximos ao verificado nas operações industriais. Neste trabalho é apresentada a técnica de identificação de parâmetros baseado num processo de estampagem profunda. A análise de sensibilidade é avaliada utilizando um método de diferenças finitas modificado e o processo de otimização utiliza programação quadrática seqüencial. Estudam-se os resultados de análise de sensibilidade utilizando os métodos de diferenças finitas tradicional e modificado, sujeitos a incrementos de tempo automático e imposto. Observa-se que a aplicação do método modificado fornece maior eficácia na aplicação da estratégia de incremento de tempo automática, além de permitir o uso de uma faixa mais ampla de fatores de penalização para o contato e de resultar em maior eficiência numérica. Vários problemas de identificação são apresentados, mostrando concordância qualitativa com os resultados disponíveis em publicações da literatura correlata. Dificuldades são encontradas na determinação simultânea de vários parâmetros devido à presença de regiões planas ou de mínimos locais no espaço de projeto, sugerindo a futura combinação da abordagem proposta neste trabalho com algoritmos evolucionários.

This work presents an algorithm able to identify all electrical parameters of three phase induction motor, with discrete realization, using a fixe-point digital signal processor based platform. Some techniques presents in the literature are analyzed for comparison and validation with proposed algorithm. Initially, an historical review about the main parameter identification algorithms is accomplished and then, is obtained the models for an induction motor. From the machine model, two parameters identification algorithms are designed: a classical RLS identification, which is widely used in literature and a robust model reference adaptive controller, objecting to ponder the unmodeled dynamics. In the development of this work are displayed simulation results using the Matlab® software, real-time simulation in DSP platform, and finally, experimental results. After this results analysis, it is possible to determinate which of results these identification techniques better represent the behavior of three phase induction motor analyzed. / Neste trabalho é desenvolvido um algoritmo capaz de identificar todos os parâmetros elétricos de um motor de indução trifásico, com realização discreta no tempo, utilizando plataforma com base em um processador digital de sinais de pontofixo. Algumas técnicas existentes na literatura são analisadas para fins de comparação e validação do algoritmo proposto. Inicialmente, faz-se uma revisão bibliográfica de algumas técnicas de identificação de parâmetros disponíveis na literatura e em seguida são obtidos os modelos do motor de indução trifásico. A partir do modelo da máquina foram projetados dois algoritmos de identificação: um identificador já conhecido na literatura do tipo mínimos quadrados recursivo (RLS) e, com o objetivo de mitigar a influência das dinâmicas não modeladas, um controlador adaptativo robusto por modelo de referência (RMRAC) é utilizado na identificação. No desenvolvimento deste trabalho, resultados de simulações utilizando o software Matlab®, simulações em tempo-real em plataforma DSP, e por fim, resultados experimentais são apresentados. A partir da análise dos resultados parte-se para a avaliação para determinar qual identificador resulta em parâmetros que melhor representa o comportamento dinâmico do motor de indução trifásico ensaiado.

It is widely accepted that correct system modeling and identification are among the most important issues power system operators face when managing instability and post-contingency scenarios. The latter is usually performed involving special computational tools that allow the operator to forecast, prevent system failure and take appropriate actions according to protocols for different contingency cases in the system. To ensure that operators make the correct simulation-based decisions, the power system models have to be validated continuously. This thesis investigates power system modeling, identification and validation problems that are formulated and based on data provided by operators, and offers new methods and deeper insight into stages of an identification cycle considering the specifics of power systems. One of the problems this thesis tackled is the selection of a modeling and simulation environment that provides transparency and possibility for unambiguous model exchange between system operators. Modelica as equation-based language fulfills these requirements. In this thesis Modelica phasor time domain models were developed and software-to-software validated against conventional simulation environments, i.e. SPS/Simulink and PSAT in MATLAB. Parameter estimation tasks for Modelica models require a modular and extensible toolbox. Thus, RaPiD Toolbox, a framework that provides system identification algorithms for Modelica models, was developed in MATLAB. Contributions of this thesis are an implementation of the Particle Filter algorithm and validation metrics for parameter identification. The performance of the proposed algorithm has been compared with Particle Swarm Optimization (PSO) algorithm when combined with simplex search and parallelized to get computational speed up. The Particle Filter outperformed PSO when estimating turbine-governor model parameters in the Greek power plant model relying on real measurements. This thesis also analyses different model structures (Nonlinear AutoRegressive eXogenous (NARX) model, Hammerstein-Wiener model, and high order transfer function) that are selected to reproduce nonlinear dynamics of a Static VAR Compensator (SVC) under incomplete information available for National Grid system operator. The study has shown that standard SVC model poorly reproduces the measured dynamics of the real system. Therefore, black-box mathematical modeling and identification approach has been proposed to solve the problem. Also, the introduced combination of first-principle and black-box approach has shown the best output fit. The methodology following identification cycle together with model order selection and model validation issues was presented in detail. Finally, one of the major contributions is a new method to formulate the uncertainty of parameters estimated in the form of a multimodal Gaussian mixture distribution that is estimated from the Particle Filter output by applying statistical methods to select the standard deviations. The proposed methodology gives additional insight into power system properties when estimating the parameters of the model. This allows power system analysts to decide on the design of validation tests for the chosen model. / Det är allmänt accepterat att korrekt modellering och identifiering av systemet är bland de mest viktiga utmaningarna som kraftsystemoperatörer ställs inför när de hanterar scenarior med instabiliteter och oförutsedda händelser. Det senare är vanligen hanterat med speciella beräkningsverktyg som låter operatören förutse utvecklingen och utföra lämpliga åtgärder enligt de protokoll som finns vid olika systemhändelser. För att försäkra sig om att operatörer tar de korrekta, simuleringsbaseda besluten måste kraftsystemsmodellen kontinuerligt valideras. Denna avhandling undersöker problem inom modellering, identifiering och validering av kraftsystem, formulerade och baserade på data tillhandahållet av operatörer, samt erbjuder nya metoder och fördjupade insikter i delar av en identifieringscykel som beaktar kraftsystemets. Ett av de problem som denna avhandling tar upp är val av en programmiljö för simulering och modellering som ger transparens och möjlighet till otvetydigt modellutbyte mellan systemoperatörer. Modelica är ett ekvationsbaserat programspråk som uppfyller dessa krav. I denna avhandling utvecklades enfasekvivalenter i Modelica som blev validerade mot konventionella program för simulering, såsom SPS/Simulink och PSAT i MATLAB. Parameterestimering i Modelica-modellerna kräver en modulär och utbyggbar verktygslåda. Därför har verktyget RaPiD Toolbox, som tillhandahåller systemidentifieringsalgoritmer för Modelica-modeller, utvecklats i MATLAB. Bidrag från denna avhandling är en implementation av ett partikelfilter (en sekventiell Monte Carlo-metod) och valideringsmetrik för parameteridentifiering. Prestandan i den föreslagna algoritmen har jämförts med partikelsvärmoptimering (PSO) då den är kombinerad med simplexsök och parallellisering. Partikelfiltret överträffade PSO när modellparametrar i turbinregulatorn i ett grekiskt kraftverk skulle estimeras utifrån verklig mätdata.  Avhandling analyserar också olika modellstrukturer (NARX, Hammerstein-Wiener-modeller, och överföringsfunktioner med höga ordningstal) som används för att reproducera den ickelinjära dynamiken hos statiska reaktiv effekt-kompenserare (SVC) vid ofullständig information som är tillgänglig för systemoperatören National Grid. Undersökningen visar att den vanliga SVC-modellen är dålig på att reproducera den verkliga, uppmätta dynamiken. Genom att matematiskt modellera problemet som en svart låda har en identifieringsmetod föreslagits. Vidare, genom att kombinera modelleringen som en svart låda med fysikaliska principer har givit den bästa anpassningen till utdata. Metodologin för identifieringscykeln tillsammans med valet av modellkomplexitet och svårigheter med modellvalidering har utförligt presenterats. Slutligen, ett av de främsta bidragen är en ny metod för att formulera osäkerheten i parameteruppskattningarna i form av en blandning av normalfördelningar med flera typvärden som estimeras med partikelfiltrets utdata genom att använda statistiska metoder för att välja standardavvikelsen. Detta ger kraftsystemanalytiker möjlighet att utforma valideringstest för den valda modellen. / <p>QC 20171121</p> / EU FP7 iTesla project

Orientador: Jose Luiz Antunes de Oliveira e Sousa / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-07T20:17:01Z (GMT). No. of bitstreams: 1 Almeida_LuizCarlosde_D.pdf: 2783638 bytes, checksum: 47822aa8fa42d03820ad07cb23b721a2 (MD5) Previous issue date: 2006 / Resumo: Esse trabalho pretende contribuir para a interpretação do comportamento de estruturas de concreto a partir da utilização de técnicas de análise inversa. Estas técnicas permitem a determinação consistente dos diversos parâmetros envolvidos em seus modelos matemáticos, tomando-se por base a observação de estruturas de concreto. A utilização desses procedimentos permite a identificação de parâmetros envolvidos no cálculo de deformações e deslocamentos das estruturas de concreto armado. Para este fim foi desenvolvido um programa computacional para identificação desses parâmetros integrando a análise via elementos finitos e a minimização da função erro estabelecida entre as variáveis calculadas e as medidas. O programa foi testado com dados de ensaios e modelos teóricos, para materiais com comportamento elástico linear isotrópico ou ortotrópico, embora o método de estimativas de parâmetros, de forma iterativa e incremental, seja também aplicável a problemas com não-linearidades. Neste trabalho o método é aplicado também para ajustes de modelos de fluência em concreto. Apresentam-se, por último, a relevância do sistema desenvolvido, bem como algumas perspectivas para complementações futuras / Abstract: This work is intended to contribute to the interpretation of concrete structures using inverse analysis techniques. These techniques allow a consistent determination of the several parameters involved in the mathematical models, starting from the observation of concrete structures. The use of these procedures led to the identification of the parameters involved in the computation of strains and displacements of reinforced concrete structures. For this, a computational program has been developed to identify the parameters, integrating the finite element analysis and the minimization of the error between computed and observed variables. The program has been validated with test data and theoretical models for linear elastic, isotropic or anisotropic materials, although the parameter estimation method is applicable also to nonlinear problems. In this work, the method is applied also to fit creep models for concrete. The main conclusions and perspectives for future development are presented. / Doutorado / Engenharia de Estruturas / Doutor em Engenharia Civil

The diploma thesis deals with control of rotary inverted pendulum - Furuta pendulum. Solution for power electronics, sensors and coupling with PC is described, identification of parameters and nonlinear simulation model in Matlab/Simulink and SimMechanics toolbox is presented. Second type Lagrange equation is used for determination of equations of motion. Controll system based on state-space model of mechanism and LQR algorithm for design of state-space controller is used and switching between swing-up cotroller a stabilizing state-space control is achieved according to actual angular position of pendulum's angle. Input integrator eliminating steady state error was used with success.

In this paper we discuss the stable solvability of the inverse problem of parameter identification in a jump diffusion model. Therefore we introduce the forward operator of this inverse problem and analyze its properties. We show continuity of the forward operator and stability of the inverse problem provided that the domain is restricted in a specific manner such that techniques of compact sets can be exploited. Furthermore, we show that there is an asymptotical non-injectivity which causes instability problems whenever the jump intensity increases and the jump heights decay simultaneously.

In this note, we consider an inverse problem in a jump diffusion model. Using characteristic functions we prove the injectivity of the forward operator mapping the five parameters determining the model to the density function of the return distribution.

Finite element simulation of thermoplastic components is gaining importance as the companies aim to avoid overdesign of the components. Cost of the component can be minimized by using an adequate amount of material for its application. Life of the component, in a particular application, can be predicted as early as during its design phase with the help of computer simulations. To achieve reliable simulation results, an accurate material model which can predict the material behaviour is vital. Most material models consist of a number of material parameters that needs to be fed into them. These material parameters can be identified with the inputs from physical tests. The accuracy of the data extracted from the physical tests, however, remains the base for the aforementioned process. The report deals with the implementation of optical measurement technique such as Digital Image Correlation (DIC) in contrast with the conventional extensometers. A tensile test is conducted on a glass fibre reinforced thermoplastic specimen, according to ISO 527-2/1A, to extract the experimental data with the help of DIC technique. The material behavior is reproduced within a finite element analysis software package LS-DYNA, with the combination of elastoplastic model called *MAT_024 and stress state dependent damage and failure model called GISSMO. The tensile test is performed under quasi-static condition to rule out the strain rate dependency of the thermoplastic material. The mesh sensitivity of the damage model is taken into account with the element size regularization. The thesis concerns setting up a routine for material parameter identification of thermoplastics by full-field calibration (FFC) approach. Also, comparison of the strain field in the specimen, obtained through the newly set up routine against the regular non-FFC i.e. extensometer measurement routine. The major objective being, through the comparisons, a qualitative assessment of the two routines in terms of calibration time vs. gain in simulation accuracy. Material models obtained through both the routines are implemented in three-point and four-point bending simulations. The predicted material behaviors are evaluated against experimental tests.

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