Dissertations / Theses on the topic 'Linearization method'

Base isolation system, as one of the most popular means to mitigate the seismic risks, often exhibits strong nonlinearity. To simplify the procedure of structural design, bilinear force-deformation behavior is recommended for isolation systems in most modern structural codes. Although base isolation system can be analyzed through nonlinear time history method, solving of a system with a large number of degrees of freedom may require an exorbitant amount of time. As a substitute, the equivalent linearization method is frequently used. Apparently, under given earthquake ground motions, the accuracy of equivalent linearization analysis method is significantly related to the estimation of equivalent linear properties. How to improve the estimation accuracy of this approximate method constitutes a subject of wide and deep interest among researchers around the world. In this research, the equivalent linearization analysis method for base-isolated buildings was investigated. The literature survey on related aspects of base-isolated buildings was carried out firstly. Then, the estimation accuracy of fifteen equivalent linearization methods selected from the literatures was evaluated when subjected to twelve earthquake ground motions. After that, from simplicity to complexity, the base-isolated buildings were modeled using single-degree-of-freedom (SDOF) systems and multi-degree-of-freedom (MDOF) systems, respectively. For both considered systems, more comprehensive parametric analyses were performed with varying the parameters selected from the isolation system and the superstructure. Accordingly, improved equivalent linearization methods were derived for SDOF and MDOF systems to improve the prediction accuracy of the maximum displacement of isolation systems. Based on the proposed equivalent linearization methods, different analysis methods for base-isolated buildings were assessed, including equivalent static linear analysis, response spectral analysis, linear and nonlinear time history analyses. It was found that with the proposed equivalent linearization methods equivalent linear analyses could yield more accurate results when compared with the equivalent linearization method recommended by structural codes. As a result, the proposed equivalent linearization method could be potentially useful for the design and analysis of baseisolated buildings, as least in the preliminary stage of structural design.

Base isolation system, as one of the most popular means to mitigate the seismic risks, often exhibits strong nonlinearity. To simplify the procedure of structural design, bilinear force-deformation behavior is recommended for isolation systems in most modern structural codes. Although base isolation system can be analyzed through nonlinear time history method, solving of a system with a large number of degrees of freedom may require an exorbitant amount of time. As a substitute, the equivalent linearization method is frequently used. Apparently, under given earthquake ground motions, the accuracy of equivalent linearization analysis method is significantly related to the estimation of equivalent linear properties. How to improve the estimation accuracy of this approximate method constitutes a subject of wide and deep interest among researchers around the world. In this research, the equivalent linearization analysis method for base-isolated buildings was investigated. The literature survey on related aspects of base-isolated buildings was carried out firstly. Then, the estimation accuracy of fifteen equivalent linearization methods selected from the literatures was evaluated when subjected to twelve earthquake ground motions. After that, from simplicity to complexity, the base-isolated buildings were modeled using single-degree-of-freedom (SDOF) systems and multi-degree-of-freedom (MDOF) systems, respectively. For both considered systems, more comprehensive parametric analyses were performed with varying the parameters selected from the isolation system and the superstructure. Accordingly, improved equivalent linearization methods were derived for SDOF and MDOF systems to improve the prediction accuracy of the maximum displacement of isolation systems. Based on the proposed equivalent linearization methods, different analysis methods for base-isolated buildings were assessed, including equivalent static linear analysis, response spectral analysis, linear and nonlinear time history analyses. It was found that with the proposed equivalent linearization methods equivalent linear analyses could yield more accurate results when compared with the equivalent linearization method recommended by structural codes. As a result, the proposed equivalent linearization method could be potentially useful for the design and analysis of baseisolated buildings, as least in the preliminary stage of structural design.

In modern wireless communication systems, advanced modulation techniques are used to support more users by handling high data rates and to increase the utilization efficiency of the limited RF spectrum. These techniques are sensitive to the nonlinear distortions due to their high peak to average power ratios. Main source of nonlinear distortion in transmitter topologies are power amplifiers that determine the overall efficiency and linearity of the transmitter. To increase linearity without sacrificing efficiency, power amplifier linearization techniques may be a choice. Baseband predistortion technique is known to be one of the optimum methods due to its relatively low complexity and its convenience for adaptation. In this thesis, different memoryless baseband signal predistortion methods are investigated and analyzed by simulations. Look-Up Table(LUT) and Polynomial approaches are compared and LUT approach is found to be better in performance. Parameters, like indexing, training sequences and training duration are evaluated. An open loop testbench is built with a real amplifier and a different LUT predistortion method that is based on amplifier modeling is offered. It is evaluated by using two tone test and adjacent channel power suppression with 8PSK data. Also, some Look-Up Table parameters are re-investigated with the proposed method. The performances of the proposed method in dierent amplifier classes are observed. Along with these studies, a list of prerequisites for design of a predistortion system is determined.

MARINHA DO BRASIL
O presente trabalho apresenta uma estrutura balanceada em quadratura para linearização de amplificadores de potência em RF e microondas. Várias técnicas de linearização têm sido utilizadas para reduzir a intermodulação. Alguns exemplos, tais como Feedback, Pre-distorsion e Feedforward, podem ser mencionados. A característica ímpar de nosso arranjo é que ele não precisa de ajustes, enquanto que os outros métodos precisam. A desvantagem de nosso arranjo é que ele reduz apenas os produtos de intermodulação de terceira ordem. Um trabalho prático foi conduzido, mostrando que nosso arranjo é capaz de reduzir o conteúdo de intermodulação de terceira ordem em até 17 dB.
The present work introduces a quadrature balanced structure for linearization of RF and microwave amplifiers. Several linearization techniques have been used to reduce intermodulation products. Some examples such as Feedback, Pre-distorsion and Feedforward may be mentioned. The unique feature of our arrangment is that it does not need adjustments, while the other methods do. The drawback of our arrangement is that it only reduces the third-order intermodulation products. A pratical work was carried out, showing that our arrangement is able to reduce the third-order intermodulation content up to 17 dB.
EL presente trabajo presenta una extructura balanceada en cuadratura para linealización de amplificadores de potencia en RF y microondas. Varias técnicas de linealización han sido utilizadas para reducir la intermodulación. Algunos ejemplos como Feedback, Pre-distorsion y Feedforward, pueden ser mencionados. La principal ventaja de nuestro arreglo frente a los otros métodos es que éste no precisa de ajustes. La desventaja de nuestro arreglo es que reduce solamente los produtos de intermodulación de tercer orden. Se condujo un trabajo práctico, mostrando que nuestro arreglo es capaz de reducir el contenido de intermodulación de tercera orden en hasta 17 dB.

The device optimization is a very important element in semiconductor technology advancement. Its objective is to find a design point for a semiconductor device so that the optimized design goal meets all specified constraints. As in other engineering fields, a nonlinear optimizer is often used for design optimization. One major drawback of using a nonlinear optimizer is that it can only partially explore the design space and return a local optimal solution. This dissertation provides an adaptive optimization design methodology to allow the designer to explore the design space and obtain a globally optimal solution. One key element of our method is to quickly compute the set of all feasible solutions, also called the acceptability region. We described a polytope-based representation for the acceptability region and an adaptive linearization technique for device performance model approximation. These efficiency enhancements have enabled significant speed-up in estimating acceptability regions and allow acceptability regions to be estimated for a larger class of device design tasks. Our linearization technique also provides an efficient mechanism to guarantee the global accuracy of the computed acceptability region. To visualize the acceptability region, we study the orthogonal projection of high-dimensional convex polytopes and propose an output sensitive algorithm for projecting polytopes into two dimensions.

Variation analysis, or tolerance analysis as it is sometimes called, is typically used to predict variation in critical dimensions in assemblies by calculating the stack-up of the contributing component variations. It is routinely used in manufacturing and assembly environments with great success. Design engineers are able to account for the small changes in dimensions that naturally occur in manufacturing processes, in equipment, and due to operators and still ensure that the assemblies will meet the design specifications and required assembly performance parameters. Furthermore, geometric variation not only affects critical fits and clearances in static assemblies, it can also cause variation in the motion of mechanisms, and their dynamic performance. The fact that variation and motion analysis are both dependent upon the geometry of the assembly makes this area of study much more challenging. This research began while investigating a particular application of dynamic assemblies - automobiles. Suspension and steering systems are prime examples dynamic assemblies. They are also critical systems, for which small changes in dimension can cause dramatic changes in the vehicle performance and capabilities. The goals of this research were to develop the tools necessary to apply the principles of static variation analysis to the kinematic motions of mechanisms. Through these tools, suspension and steering systems could be analyzed over a range of positions to determine how small changes in dimensions could affect the performance of those systems. There are two distinct applications for this research, steering systems and suspension systems. They are treated separately, as they have distinct requirements. Steering systems are mechanisms, for which position information is most critical to performance. In suspension systems, however, the higher order kinematic terms of velocity and acceleration often are more important than position parameters.

In this thesis we mainly focused on the usage of the Conditional Value-at-Risk (CVaR) in risk management and on the pricing of the arithmetic average basket and Asian options in the Black-Scholes framework via a new log-normal sum approximation method. Firstly, we worked on the linearization procedure of the CVaR proposed by Rockafellar and Uryasev. We constructed an optimization problem with the objective of maximizing the expected return under a CVaR constraint. Due to possible intermediate payments we assumed, we had to deal with a re-investment problem which turned the originally one-period problem into a multiperiod one. For solving this multi-period problem, we used the linearization procedure of CVaR and developed an iterative scheme based on linear optimization. Our numerical results obtained from the solution of this problem uncovered some surprising weaknesses of the use of Value-at-Risk (VaR) and CVaR as a risk measure. In the next step, we extended the problem by including the liabilities and the quantile hedging to obtain a reasonable problem construction for managing the liquidity risk. In this problem construction the objective of the investor was assumed to be the maximization of the probability of liquid assets minus liabilities bigger than a threshold level, which is a type of quantile hedging. Since the quantile hedging is not a perfect hedge, a non-zero probability of having a liability value higher than the asset value exists. To control the amount of the probable deficient amount we used a CVaR constraint. In the Black-Scholes framework, the solution of this problem necessitates to deal with the sum of the log-normal distributions. It is known that sum of the log-normal distributions has no closed-form representation. We introduced a new, simple and highly efficient method to approximate the sum of the log-normal distributions using shifted log-normal distributions. The method is based on a limiting approximation of the arithmetic mean by the geometric mean. Using our new approximation method we reduced the quantile hedging problem to a simpler optimization problem. Our new log-normal sum approximation method could also be used to price some options in the Black-Scholes model. With the help of our approximation method we derived closed-form approximation formulas for the prices of the basket and Asian options based on the arithmetic averages. Using our approximation methodology combined with the new analytical pricing formulas for the arithmetic average options, we obtained a very efficient performance for Monte Carlo pricing in a control variate setting. Our numerical results show that our control variate method outperforms the well-known methods from the literature in some cases.

Generalisation de la methode iterative sous contrainte de regularite a des equations integrales non lineaires et singulieres, a des equations integrodifferentielles, differentielles et aux derivees partielles. Comparaison entre les resultats numeriques et les solutions theoriques. Insertion d'une contrainte supplementaire a la contrainte de regularite pour le traitement des problemes non lineaires a plusieurs solutions. Exemples numeriques

Le problème de conception d'avant-projet des structures mécaniques complexes soumis au double impératif de qualité et de rapidité est de plus en plus difficile à appréhender. Il offre un terrain très favorable à la synthèse automatique par le biais de l'optimisation mathématique. Fort de ce constat, nous étudions le potentiel d'utilisation de l'optimisation mathématique dans la phase de conception d'avant-projet. Notre étude se décompose en deux étapes: l'élaboration d'un outil informatique adapté et son exploitation dans le contexte de la conception d'avant-projet des structures de véhicules de transport guidés. L’outil informatique proposé s'appuie sur des techniques d'optimisation éprouvées et respecte les exigences de l'optimisation des structures d'avant-projets. Il met en œuvre la méthode des différences finies pour le calcul des sensibilités paramétriques et la méthode à linéarisation convexe de C. Fleury pour l'optimisation proprement dite. Des améliorations sont apportées à cette dernière et une recherche linéaire appropriée est développée. Trois tests simples démontrent le bien fondé des modifications effectuées. L’exploitation de l'outil proposé est conduite à partir de l'optimisation sous contraintes statiques et dynamiques de quatre structures à caractère industriel. Des simulations du processus de conception et de rédaction d'offres incluant des éléments issus de l'optimisation illustrent les résultats obtenus. L’utilisation judicieuse de l'optimisation et l'exploitation fine de ses résultats fournit rapidement au concepteur des réponses fiables à ses interrogations et devrait lui permettre de conduire efficacement les premiers pas de son projet ou encore de produire en temps limite des offres très compétitives

Nowadays the developments of power supplies in military, industrial or commercial applications are growing rapidly, not only to achieve the highest efficiency but also to focus on the size and weight minimization which are playing a major role in this area. Therefore, the research trends in dc-dc, ac-dc, dc-ac, ac-ac topologies are still continuously developing into the direction of new topologies, new control concepts, new materials and devices to achieve highest efficiency and smallest size. The cost per unit is also one of the most important points of power supplies. Also, with new control methods and new ways of manufacturing, for example, the cost per unit might be reduced. Also, a simplified control concept might help to avoid discrete circuits, especially, at low power levels. The last mentioned statement is demonstrated, for instance, by the concept of the Link-Switch of the company Power Integration where an extremely small number of components are necessary. With the target of minimization, this research work explores the possibility to replace conventional electromagnetic transformers considered as the most bulky devices in power supplies by piezoelectric transformers (PT) for innovative off-line power supplies. Several control methods for a load resonant converter focusing on class-E topology utilizing PT, were developed in order to investigate and to select an appropriate control method capable of improving the efficiency and reducing the size of the converter. Efficiency should be understood in this way as maximum reliability at minimum power losses. Different controllers were evaluated for optimizing the effect of disturbances of line and load variations. The ZVS condition for a wide input voltage range and a wide output load range can be achieved by a method called duty-cycle tracking. Further, with an improved design of the PT containing an auxiliary tap, the ZVS condition can be obtained by a method called turn-on synchronization. The controlled output voltage, current or power is achieved by a variable frequency control. Further, the dynamic modeling for open loop and closed loop of load resonant converters, focused on the class-E topology, was introduced. The transient behavior of the output voltage of the open loop against perturbations such as the input voltage change, the switching frequency change, and the output load change is treated by replacing the complete circuit of the class-E converter by simple equivalent circuit models. The results from the analysis of the open loop dynamic behavior are applied to modeling the closed loop class-E converter with several control methods. The methods of linearization for exact solution and heuristic approximation for the steady state analysis were purposed. These models of linearization were implemented with the controller in its topologies to investigate the sufficient accuracy of obtained results of the regulation. Besides, the linearization models were used to observe the stability condition of the proposed control loops. Finally, the evaluation of a well-known classical control such P, I, PI, PD, PID and a simplified controller for a fixed load application by matching an appropriate switching frequency according to the input voltage, into the load resonant converter, considering class-E topology, were presented. Also, the optimum design of the controller for a load resonant converter was discussed and derived
Die Entwicklung von Stromversorgungen in militärischen, industriellen und kommerziellen Anwendungen nimmt bis heute tendenziell stark zu. Nicht nur zur Erzielung höchster Wirkungsgrade, sondern auch im Hinblick auf Baugrößen- und Gewichtsminimierung, welche eine vorrangige Rolle spielen, ist diese Tendenz zu verzeichnen. Diesbezüglich gehen die Forschungstrends bei DC-DC, AC-DC, DC-AC und AC-AC Topologien in Richtung neuer Topologien, neuer Regelungskonzepte, sowie neuer Materialien und Bauelemente, um den höchsten Wirkungsgrad bei kleinster Baugröße zu erreichen. Die Gerätekosten sind ebenso ein sehr wichtiger Punkt bei Stromversorgungen. Auch durch neue Regelungsmethoden und durch neue Herstellungsverfahren können die Gerätekosten beispielsweise reduziert werden. Ebenso kann ein vereinfachtes Regelungskonzept dazu verhelfen, dass diskrete Schaltungen, speziell im unteren Leistungsbereich, vermieden werden. Letzteres wird beispielsweise beim Konzept des Link-Switch der Firma Power Integration verdeutlicht, indem extern wenige Bauelemente benötigt werden. Mit dem Ziel der Miniaturisierung wird in dieser Forschungsarbeit die Möglichkeit untersucht, konventionelle elektromagnetische Transformatoren, welche in Stromversorgungen als besonders voluminös gelten, durch piezoelektrische Transformatoren (PT) bei der Herstellung innovativer Netzstromversorgungen zu ersetzen. Verschiedene Regelungsmethoden für Lastresonanzkonverter, mit dem Fokus auf eine Klasse- E-Topologie mit PT, wurden hierzu entwickelt. Dies hatte zum Ziel, ein geeignetes Regelungsverfahren zu erarbeiten und auszuwählen, welches eine verbesserte Effizienz bei reduzierter Konverter-Baugröße aufzuweisen hat. Effizienz soll hierbei verstanden werden als maximale Zuverlässigkeit bei minimalen Leistungsverlusten. Verschiedene Reglertypen wurden entworfen um die Effekte der Störungen durch Netzspannungs-und Lastvariationen regelungstechnisch zu optimieren. Die Nullspannungsschaltungsbedingung (ZVS-Bedingung) über einen weiten Bereich der Eingangspannung und einen weiten Lastbereich kann durch einen sogenannte Duty-Cycle-Nachführung mit der Frequenz erreicht werden. Weiterhin kann durch eine verbesserte Ausführung des PT auf Basis einer Hilfsanzapfung die ZVSBedingung durch eine sogenannte Einschaltsynchronisation erreicht werden. Geregelte Ausgangsspannung, Ausgangsstrom oder Ausgangsleistung werden über eine Frequenzstellung erreicht. Die dynamische Modellierung der offenen und geschlossenen Regelschleife eines Lastresonanzkonverters, wieder im Hinblick auf die Klasse-E, wird im weiteren vorgestellt. Das transiente Verhalten der Ausgangsspannung der offenen Regelschleife gegenüber Störungen durch Eingangsspannungsänderung, durch Schaltfrequenzänderung oder durch Ausgangslaständerung, wird durch den Ersatz der Klasse-E-Schaltung durch einfache Äquivalenzmodelle behandelt. Die Ergebnisse der Analyse des Verhaltens des offenenen Regelkreises werden verwendet, um den Klasse-E-Konverter mit geschlossener Regelschleife unter Verwendung verschiedener vorgestellter Regelungsmethoden zu modellieren. Methoden der Linearisierung für die exakte Lösung und für eine heuristische Approximation der statischen Analyse des eingeschwungenen Zustands werden vorgeschlagen. Diese Methoden der Linearisierung werden zusammen mit den Reglermodellen in deren jeweilige Topologie implementiert um die ausreichende Genauigkeit der erhaltenen Resultate des Regelungsverhaltens zu beurteilen. Weiterhin werden diese Linearisierungsmodelle dazu verwendet, die Stabilitätskriterien der vorgeschlagenen Regelschleife zu überwachen. Schlussendlich wird die Bestimmung der bekannten klassischen Regler (P, I, PI, PD, PID), sowie eines vereinfachten Konstantlaststellers durch geeignete Anpassung der Schaltfrequenz an die Eingangsspannung, für Lastresonanzkonverter, wieder mit Blick auf die Klasse-E, vorgestellt. Außerdem wird der optimierte Reglerentwurf für Lastresonanzkonverter diskutiert und abgeleitet

Exactly constrained (EC) design is a robust design method which can be used for mechanical assemblies. It entails using the minimum number of constraints to eliminate all desired motion. While found by some engineers in industry to have many benefits (including robust assembly, no binding or play, ease of assembly, and the ability to tolerate the wear of parts), EC designs remain somewhat unrecognized by academia. One reason for this minimal exposure may be the lack of a quantitative foundation for such designs. This thesis describes the history and current background for EC designs, and it also begins to develop a quantitative foundation for EC design based on several mathematical methods. EC designs can be analyzed quite simply by understanding that they are statically determinate. Because of this, the equations of equilibrium can be used to validate the rules and the nesting force window that have been defined by Blanding [1999]. In addition, a generalized method using the equations of equilibrium has been developed in this thesis to analyze an EC design based on the locations of the constraints and to find the nesting force window. The direct linearization method (DLM) is another mathematical method used to quantify information in an EC design. While EC designs provide many advantages, some EC assemblies may be "better" than others. A quantitative measure of goodness is developed in this thesis using the DLM. The goodness value assigned to each design through this process can either be used to make a decision on an individual design, or it can be used to compare similar EC designs. Finally, the robust nature of EC design is examined using a Monte Carlo simulation. In general, the results show that EC designs have a higher rate of assembly than similar designs that are over-constrained. They are more robust. In addition, EC designs have lower assembly error than the similarly over-constrained assemblies.

Nowadays the developments of power supplies in military, industrial or commercial applications are growing rapidly, not only to achieve the highest efficiency but also to focus on the size and weight minimization which are playing a major role in this area. Therefore, the research trends in dc-dc, ac-dc, dc-ac, ac-ac topologies are still continuously developing into the direction of new topologies, new control concepts, new materials and devices to achieve highest efficiency and smallest size. The cost per unit is also one of the most important points of power supplies. Also, with new control methods and new ways of manufacturing, for example, the cost per unit might be reduced. Also, a simplified control concept might help to avoid discrete circuits, especially, at low power levels. The last mentioned statement is demonstrated, for instance, by the concept of the Link-Switch of the company Power Integration where an extremely small number of components are necessary. With the target of minimization, this research work explores the possibility to replace conventional electromagnetic transformers considered as the most bulky devices in power supplies by piezoelectric transformers (PT) for innovative off-line power supplies. Several control methods for a load resonant converter focusing on class-E topology utilizing PT, were developed in order to investigate and to select an appropriate control method capable of improving the efficiency and reducing the size of the converter. Efficiency should be understood in this way as maximum reliability at minimum power losses. Different controllers were evaluated for optimizing the effect of disturbances of line and load variations. The ZVS condition for a wide input voltage range and a wide output load range can be achieved by a method called duty-cycle tracking. Further, with an improved design of the PT containing an auxiliary tap, the ZVS condition can be obtained by a method called turn-on synchronization. The controlled output voltage, current or power is achieved by a variable frequency control. Further, the dynamic modeling for open loop and closed loop of load resonant converters, focused on the class-E topology, was introduced. The transient behavior of the output voltage of the open loop against perturbations such as the input voltage change, the switching frequency change, and the output load change is treated by replacing the complete circuit of the class-E converter by simple equivalent circuit models. The results from the analysis of the open loop dynamic behavior are applied to modeling the closed loop class-E converter with several control methods. The methods of linearization for exact solution and heuristic approximation for the steady state analysis were purposed. These models of linearization were implemented with the controller in its topologies to investigate the sufficient accuracy of obtained results of the regulation. Besides, the linearization models were used to observe the stability condition of the proposed control loops. Finally, the evaluation of a well-known classical control such P, I, PI, PD, PID and a simplified controller for a fixed load application by matching an appropriate switching frequency according to the input voltage, into the load resonant converter, considering class-E topology, were presented. Also, the optimum design of the controller for a load resonant converter was discussed and derived.
Die Entwicklung von Stromversorgungen in militärischen, industriellen und kommerziellen Anwendungen nimmt bis heute tendenziell stark zu. Nicht nur zur Erzielung höchster Wirkungsgrade, sondern auch im Hinblick auf Baugrößen- und Gewichtsminimierung, welche eine vorrangige Rolle spielen, ist diese Tendenz zu verzeichnen. Diesbezüglich gehen die Forschungstrends bei DC-DC, AC-DC, DC-AC und AC-AC Topologien in Richtung neuer Topologien, neuer Regelungskonzepte, sowie neuer Materialien und Bauelemente, um den höchsten Wirkungsgrad bei kleinster Baugröße zu erreichen. Die Gerätekosten sind ebenso ein sehr wichtiger Punkt bei Stromversorgungen. Auch durch neue Regelungsmethoden und durch neue Herstellungsverfahren können die Gerätekosten beispielsweise reduziert werden. Ebenso kann ein vereinfachtes Regelungskonzept dazu verhelfen, dass diskrete Schaltungen, speziell im unteren Leistungsbereich, vermieden werden. Letzteres wird beispielsweise beim Konzept des Link-Switch der Firma Power Integration verdeutlicht, indem extern wenige Bauelemente benötigt werden. Mit dem Ziel der Miniaturisierung wird in dieser Forschungsarbeit die Möglichkeit untersucht, konventionelle elektromagnetische Transformatoren, welche in Stromversorgungen als besonders voluminös gelten, durch piezoelektrische Transformatoren (PT) bei der Herstellung innovativer Netzstromversorgungen zu ersetzen. Verschiedene Regelungsmethoden für Lastresonanzkonverter, mit dem Fokus auf eine Klasse- E-Topologie mit PT, wurden hierzu entwickelt. Dies hatte zum Ziel, ein geeignetes Regelungsverfahren zu erarbeiten und auszuwählen, welches eine verbesserte Effizienz bei reduzierter Konverter-Baugröße aufzuweisen hat. Effizienz soll hierbei verstanden werden als maximale Zuverlässigkeit bei minimalen Leistungsverlusten. Verschiedene Reglertypen wurden entworfen um die Effekte der Störungen durch Netzspannungs-und Lastvariationen regelungstechnisch zu optimieren. Die Nullspannungsschaltungsbedingung (ZVS-Bedingung) über einen weiten Bereich der Eingangspannung und einen weiten Lastbereich kann durch einen sogenannte Duty-Cycle-Nachführung mit der Frequenz erreicht werden. Weiterhin kann durch eine verbesserte Ausführung des PT auf Basis einer Hilfsanzapfung die ZVSBedingung durch eine sogenannte Einschaltsynchronisation erreicht werden. Geregelte Ausgangsspannung, Ausgangsstrom oder Ausgangsleistung werden über eine Frequenzstellung erreicht. Die dynamische Modellierung der offenen und geschlossenen Regelschleife eines Lastresonanzkonverters, wieder im Hinblick auf die Klasse-E, wird im weiteren vorgestellt. Das transiente Verhalten der Ausgangsspannung der offenen Regelschleife gegenüber Störungen durch Eingangsspannungsänderung, durch Schaltfrequenzänderung oder durch Ausgangslaständerung, wird durch den Ersatz der Klasse-E-Schaltung durch einfache Äquivalenzmodelle behandelt. Die Ergebnisse der Analyse des Verhaltens des offenenen Regelkreises werden verwendet, um den Klasse-E-Konverter mit geschlossener Regelschleife unter Verwendung verschiedener vorgestellter Regelungsmethoden zu modellieren. Methoden der Linearisierung für die exakte Lösung und für eine heuristische Approximation der statischen Analyse des eingeschwungenen Zustands werden vorgeschlagen. Diese Methoden der Linearisierung werden zusammen mit den Reglermodellen in deren jeweilige Topologie implementiert um die ausreichende Genauigkeit der erhaltenen Resultate des Regelungsverhaltens zu beurteilen. Weiterhin werden diese Linearisierungsmodelle dazu verwendet, die Stabilitätskriterien der vorgeschlagenen Regelschleife zu überwachen. Schlussendlich wird die Bestimmung der bekannten klassischen Regler (P, I, PI, PD, PID), sowie eines vereinfachten Konstantlaststellers durch geeignete Anpassung der Schaltfrequenz an die Eingangsspannung, für Lastresonanzkonverter, wieder mit Blick auf die Klasse-E, vorgestellt. Außerdem wird der optimierte Reglerentwurf für Lastresonanzkonverter diskutiert und abgeleitet.

On calcule les solutions issues des lois de conservation scalaires non linéaires à l'aide d'éléments finis discontinus en dimension un ou en dimension supérieure. On utilise des approximations constantes par morceaux pour obtenir des schémas d'ordre un et on passe à l'ordre supérieur en augmentant le degré des polynômes d'approximation. On étudie la convergence des schémas stabilisés implicites ou explicites

Tato práce je zaměřena na odhad letových parametrů malého letounu, konkrétně letounu Evektor SportStar RTC. Pro odhad letových parametrů jsou použity metody "Equation Error Method", "Output Error Method" a metody rekurzivních nejmenších čtverců. Práce je zaměřena na zkoumání charakteristik aerodynamických parametrů podélného pohybu a ověření, zda takto odhadnuté letové parametry odpovídají naměřeným datům a tudíž vytvářejí předpoklad pro realizaci dostatečně přesného modelu letadla. Odhadnuté letové parametry jsou dále porovnávány s a-priorními hodnotami získanými s využitím programů Tornado, AVL a softwarovéverze sbírky Datcom. Rozdíly mezi a-priorními hodnotami a odhadnutými letovými paramatery jsou porovnány s korekcemi publikovanými pro subsonické letové podmínky modelu letounu F-18 Hornet.

Models, modelling and control design play important parts in automatic control. The contributions in this thesis concern topics in all three of these concepts. The poles are of fundamental importance when analyzing the behaviour of a system, and pole placement is an intuitive and natural approach for control design. A novel parameterization for state feedback gains for pole placement in the linear multiple input case is presented and analyzed. It is shown that when the open and closed loop poles are disjunct, every state feedback gain can be parameterized. Other properties are also investigated. Hammerstein models have a static non-linearity on the input. A method for exact compensation of such non-linearities, combined with introduction of integral action, is presented. Instead of inversion of the non-linearity the method utilizes differentiation, which in many cases is simpler. A partial differential equation (PDE) can be regarded as an infinite order model. Many model based control design techniques, like linear quadratic Gaussian control (LQG), require finite order models. Active damping of vibrations in a viscoelastic beam, modelled as a PDE, is considered. The beam is actuated by piezoelectric elements and its movements are measured by strain gauges. LQG design is used, for which different finite order models, approximating the PDE model, are constructed. The so obtained controllers are evaluated on the original PDE model. Minimization of the measured strain yields a satisfactory performance, but minimization of transversal deflection does not. The effect of the model accuracy of the finite order model approximations is also investigated. It turns out that a model with higher accuracy in a specified frequency interval gives controllers with better performance. The wave equation is another PDE. A PDE model, with one spatial dimension, is established. It describes wave propagation in a tube perforated with helical slots. The model describes waves of both extensional and torsional type, as well as the coupling between the two wave types. Experimental data are used for estimation of model parameters, and for assessment of the proposed model in two different cases. The model is found adequate when certain geometrical assumptions are valid.

Utilizing the universal approximation property of neural networks, we develop several novel approaches to neural network-based adaptive output feedback control of nonlinear systems, and illustrate these approaches for several flight control applications. In particular, we address the problem of non-affine systems and eliminate the fixed point assumption present in earlier work. All of the stability proofs are carried out in a form that eliminates an algebraic loop in the neural network implementation. An approximate input/output feedback linearizing controller is augmented with a neural network using input/output sequences of the uncertain system. These approaches permit adaptation to both parametric uncertainty and unmodeled dynamics. All physical systems also have control position and rate limits, which may either deteriorate performance or cause instability for a sufficiently high control bandwidth. Here we apply a method for protecting an adaptive process from the effects of input saturation and time delays, known as ``pseudo control hedging". This method was originally developed for the state feedback case, and we provide a stability analysis that extends its domain of applicability to the case of output feedback. The approach is illustrated by the design of a pitch-attitude flight control system for a linearized model of an R-50 experimental helicopter, and by the design of a pitch-rate control system for a 58-state model of a flexible aircraft consisting of rigid body dynamics coupled with actuator and flexible modes. A new approach to augmentation of an existing linear controller is introduced. It is especially useful when there is limited information concerning the plant model, and the existing controller. The approach is applied to the design of an adaptive autopilot for a guided munition. Design of a neural network adaptive control that ensures asymptotically stable tracking performance is also addressed.

Táto diplomová práca sa zaoberá návrhom a konštrukciou elektromagnetickej, polohovacej platformy, pre testovanie nelineárnych riadiacich a identifikačných algoritmov. Platforma je založená na tvarovaní magnetického poľa v každom bode pomocou troch elektromagnetov a polohuje oceľovú guličku po dotykovom paneli ktorý sníma polohu tejto guličky. Platforma má slúžiť hlavne pre demonštráciu rôznych nelineárnych riadiacich algoritmov vo výukovom prostredí. Tri príklady takýchto algoritmov sú ukázané a overené v rámci tejto diplomovej práce.

Steelmaking industry, one of the most electricity-intensive industrial processes, is seeking for new approaches to improve its competitiveness in terms of energy savings by taking advantage of the volatile electricity prices. This fluctuation in the price is mainly caused by the increasing share of renewable energy sources, the liberalization of energy markets and the growing demand of the energy. Therefore, making the production scheduling of steelmaking processes with knowledge about the cost of the energy may lead to significant cost savings in the electricity bills. With this aim in mind, different models are developed in this project in order to improve the existing monolithic models (continuous-time based scheduling) to find an efficient formulation of accounting for electricity consumption and also to expand them with more detailed scheduling of Electric Arc Furnace stage in the production process. The optimization of the energy cost with multiple electricity sources and contracts and the production planning are usually done as stand-alone optimizers due to their complexity, therefore as a new approach in addition to the monolithic model an iterative framework is developed in this work. The idea to integrate the two models in an iterative manner has potential to be useful in the industry due to low effort for reformulation of existing models. The implemented framework uses multiparametric programming together with bilevel programming in order to direct the schedule to find a compromise between the production constraints and goals, and the energy cost. To ensure applicability heuristic approaches are also examined whenever full sized models are not meeting computational performance requirements. The results show that the monolithic model implemented has a considerable advantage in terms of computational time compared to the models in the literature and in some cases, the solution can be obtained in a few minutes instead of hours. In the contrary, the iterative framework shows a bad performance in terms of computational time when dealing with real world instances. For that matter a heuristic approach, which is easy to implement, is investigated based on coordination theory and the results show that it has a potential since it provides solutions close to the optimal solutions in a reasonable amount of time. Multiparametric programming is the main core of the iterative framework developed in this internship and it is not able to give the solutions for real world instances due to computational time limitations. This computational problem is related to the nature of the algorithm behind mixed integer multiparametric programming and its ability to handle the binary variables. Therefore, further work to this project is to develop new approaches to approximate multiparametric technique or develop some heuristics to approximate the mp-MILP solutions.

This dissertation addresses five fundamental resource allocation problems on networks, all of which have applications to support Homeland Security or industry challenges. In the first application, we model and solve the strategic problem of minimizing the expected loss inflicted by a hostile terrorist organization. An appropriate allocation of certain capability-related, intent-related, vulnerability-related, and consequence-related resources is used to reduce the probabilities of success in the respective attack-related actions, and to ameliorate losses in case of a successful attack. Given the disparate nature of prioritizing capital and material investments by federal, state, local, and private agencies to combat terrorism, our model and accompanying solution procedure represent an innovative, comprehensive, and quantitative approach to coordinate resource allocations from various agencies across the breadth of domains that deal with preventing attacks and mitigating their consequences. Adopting a nested event tree optimization framework, we present a novel formulation for the problem as a specially structured nonconvex factorable program, and develop two branch-and-bound schemes based respectively on utilizing a convex nonlinear relaxation and a linear outer-approximation, both of which are proven to converge to a global optimal solution. We also investigate a fundamental special-case variant for each of these schemes, and design an alternative direct mixed-integer programming model representation for this scenario. Several range reduction, partitioning, and branching strategies are proposed, and extensive computational results are presented to study the efficacy of different compositions of these algorithmic ingredients, including comparisons with the commercial software BARON. The developed set of algorithmic implementation strategies and enhancements are shown to outperform BARON over a set of simulated test instances, where the best proposed methodology produces an average optimality gap of 0.35% (compared to 4.29% for BARON) and reduces the required computational effort by a factor of 33. A sensitivity analysis is also conducted to explore the effect of certain key model parameters, whereupon we demonstrate that the prescribed algorithm can attain significantly tighter optimality gaps with only a near-linear corresponding increase in computational effort. In addition to enabling effective comprehensive resource allocations, this research permits coordinating agencies to conduct quantitative what-if studies on the impact of alternative resourcing priorities. The second application is motivated by the author's experience with the U.S. Army during a tour in Iraq, during which combined operations involving U.S. Army, Iraqi Army, and Iraqi Police forces sought to interdict the transport of selected materials used for the manufacture of specialized types of Improvised Explosive Devices, as well as to interdict the distribution of assembled devices to operatives in the field. In this application, we model and solve the problem of minimizing the maximum flow through a network from a given source node to a terminus node, integrating different forms of superadditive synergy with respect to the effect of resources applied to the arcs in the network. Herein, the superadditive synergy reflects the additional effectiveness of forces conducting combined operations, vis-à-vis unilateral efforts. We examine linear, concave, and general nonconcave superadditive synergistic relationships between resources, and accordingly develop and test effective solution procedures for the underlying nonlinear programs. For the linear case, we formulate an alternative model representation via Fourier-Motzkin elimination that reduces average computational effort by over 40% on a set of randomly generated test instances. This test is followed by extensive analyses of instance parameters to determine their effect on the levels of synergy attained using different specified metrics. For the case of concave synergy relationships, which yields a convex program, we design an inner-linearization procedure that attains solutions on average within 3% of optimality with a reduction in computational effort by a factor of 18 in comparison with the commercial codes SBB and BARON for small- and medium-sized problems; and outperforms these softwares on large-sized problems, where both solvers failed to attain an optimal solution (and often failed to detect a feasible solution) within 1800 CPU seconds. Examining a general nonlinear synergy relationship, we develop solution methods based on outer-linearizations, inner-linearizations, and mixed-integer approximations, and compare these against the commercial software BARON. Considering increased granularities for the outer-linearization and mixed-integer approximations, as well as different implementation variants for both these approaches, we conduct extensive computational experiments to reveal that, whereas both these techniques perform comparably with respect to BARON on small-sized problems, they significantly improve upon the performance for medium- and large-sized problems. Our superlative procedure reduces the computational effort by a factor of 461 for the subset of test problems for which the commercial global optimization software BARON could identify a feasible solution, while also achieving solutions of objective value 0.20% better than BARON. The third application is likewise motivated by the author's military experience in Iraq, both from several instances involving coalition forces attempting to interdict the transport of a kidnapping victim by a sectarian militia as well as, from the opposite perspective, instances involving coalition forces transporting detainees between interment facilities. For this application, we examine the network interdiction problem of minimizing the maximum probability of evasion by an entity traversing a network from a given source to a designated terminus, while incorporating novel forms of superadditive synergy between resources applied to arcs in the network. Our formulations examine either linear or concave (nonlinear) synergy relationships. Conformant with military strategies that frequently involve a combination of overt and covert operations to achieve an operational objective, we also propose an alternative model for sequential overt and covert deployment of subsets of interdiction resources, and conduct theoretical as well as empirical comparative analyses between models for purely overt (with or without synergy) and composite overt-covert strategies to provide insights into absolute and relative threshold criteria for recommended resource utilization. In contrast to existing static models, in a fourth application, we present a novel dynamic network interdiction model that improves realism by accounting for interactions between an interdictor deploying resources on arcs in a digraph and an evader traversing the network from a designated source to a known terminus, wherein the agents may modify strategies in selected subsequent periods according to respective decision and implementation cycles. We further enhance the realism of our model by considering a multi-component objective function, wherein the interdictor seeks to minimize the maximum value of a regret function that consists of the evader's net flow from the source to the terminus; the interdictor's procurement, deployment, and redeployment costs; and penalties incurred by the evader for misperceptions as to the interdicted state of the network. For the resulting minimax model, we use duality to develop a reformulation that facilitates a direct solution procedure using the commercial software BARON, and examine certain related stability and convergence issues. We demonstrate cases for convergence to a stable equilibrium of strategies for problem structures having a unique solution to minimize the maximum evader flow, as well as convergence to a region of bounded oscillation for structures yielding alternative interdictor strategies that minimize the maximum evader flow. We also provide insights into the computational performance of BARON for these two problem structures, yielding useful guidelines for other research involving similar non-convex optimization problems. For the fifth application, we examine the problem of apportioning railcars to car manufacturers and railroads participating in a pooling agreement for shipping automobiles, given a dynamically determined total fleet size. This study is motivated by the existence of such a consortium of automobile manufacturers and railroads, for which the collaborative fleet sizing and efforts to equitably allocate railcars amongst the participants are currently orchestrated by the \textit{TTX Company} in Chicago, Illinois. In our study, we first demonstrate potential inequities in the industry standard resulting either from failing to address disconnected transportation network components separately, or from utilizing the current manufacturer allocation technique that is based on average nodal empty transit time estimates. We next propose and illustrate four alternative schemes to apportion railcars to manufacturers, respectively based on total transit time that accounts for queuing; two marginal cost-induced methods; and a Shapley value approach. We also provide a game-theoretic insight into the existing procedure for apportioning railcars to railroads, and develop an alternative railroad allocation scheme based on capital plus operating costs. Extensive computational results are presented for the ten combinations of current and proposed allocation techniques for automobile manufacturers and railroads, using realistic instances derived from representative data of the current business environment. We conclude with recommendations for adopting an appropriate apportionment methodology for implementation by the industry.
Ph. D.

This thesis deals with the utilization of new principles of characterization of gate capacitances for sigma-delta modulators. Sigma-delta modulators are the integral part of sigma-delta analog-to-digital converters. The proposed new method is characterized by high resolution and modest requirements for laboratory equipment. It allows characterizing capacitances whose values are within the range which is used in sigma-delta modulators. The thesis contains description of the new method, the analysis of measurement accuracy and experimental results.

Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xix, 156 p.; also includes graphics (some col.). Includes bibliographical references (p. 152-156).

博士
國立交通大學
資訊管理研究所
96
The piecewise linearization methods have been applied in numerous applications, including data fitting, network analysis, logistics, and statistics. In the early 1950s, they have been recognized that a concave function can be linearized by introducing 0--1 variables. Most textbooks in Operations Research offer some methods of expressing linear approximations in this manner. Many methods of linearization have also been developed in recent literature. Nevertheless, the transformed linear approach often encounters a severe shortcoming. Standard procedures for linearizing typically involve a radical increase in the number of binary variables. Consequently, the gains to be derived from dealing with linear functions are quite likely to be nullified by the increased problem size. For linearizing a concave function with m break points, the conventional methods require to use m-1 binary variables. However, when m becomes large, the computation will be very time-consuming and may cause heavy computational burden. This dissertation proposes a novel technique in which only log2 (m-1) binary variables are used. The proposed method has the following features: (i) it uses more convenient and efficient way to express a piecewise linear function; (ii) less number of 0--1 variables are used; (iii) the omputational results show that the proposed method is much efficient and faster than the conventional one especially when the number of break points becomes large. The proposed method has been applied to solve the two major problems, geometric programs (GP) and nonlinear fractional programs (NFP), which are popular in engineering design and management science. The efficiency and feasibility of the proposed methods can be verified through illustrations.

碩士
國立屏東科技大學
車輛工程系所
96
In this thesis, the mathematical model and nonlinear adaptive control of a twin-rotor helicopter model system is studied. To address the attitude control problem for twin rotor helicopter system. The control objective is to keep the helicopter attitude, i.e., pitch and yaw angles, in a desired manner. In the controller design, the feedback control, sliding mode control, Lyapunov theorem, and adaptive algorithm have been used to improve couple problem and estimated parameter to achieve the control objective.

A new non-parametric linearization method for nonlinear random vibration analysis is created. This method works on a discrete representation of the stochastic inputs and the ideas from the first order reliability method (FORM). For a specifiedzresponse thresholdzof theznonlinear system, thezequivalent linearzsystem is characterizedxby matchingzthe "design points" of the linear and nonlinearzresponses in the space of thezstandard normalzvariables acquiredzfrom the discretizationzof thezexcitation. Because of thiszdefinition, the tail probabilityzofzthe linearzsystem is equalzto the firstzorder approximation ofzthe tailzprobability of theznonlinear system, this propertyzmotivating the namezTail- EquivalentzLinearization Method (TELM).This leads to the identification of the TELS in terms of a unit-impulse response function for each component of the input excitation,tail equivalent linearization method is a new,non-parametric linearization method for nonlinear random vibration analysis.This method is to overcome the inadequacy of conventional equivalent linearization method.Our objectives are investigation and thorough understanding of analysis of stochastic non-linear system by tail equivalent linearization method as well as computation of certain nonlinear response characteristics. Further more study is presented on method of random vibrational analysis especially on equivalent linearization method and also gives brief review on reliability analysis of structure, first order reliability analysis (FORM).It is demonstratedzthat the equivalentzlinear systemzis determined in termszof its impulsezresponse functionzin the non-parametriczform fromzthe knowledgezof design point. This examination lookszatzthe impacts of differentzparameters onzthe tail-equivalentzlinear system, presentszan algorithmzfor findingzthe design points. Design point in FORM is the point on a limit-state surface that is nearest to the origin when the random variables are transformed to the standard normal space.Linearization of the limit-state surface at this point uniquely defines a linear system, denoted as Tail-Equivalent Linear System, TELS.Previous study shows that design point shows that design point on limit state surface of linear system and nonlinear system is same. Once the TELS is defined for a specific response threshold, methods of linear random vibrational analysis are used to compute various response statistics, such as the mean crossing rate and tail probabilities of local and extreme peaks. The method has been developed for application in both time, and frequency domain and it has been applied to inelastic structures as well as structures experiencing geometric nonlinearities.

Leung Chi-Shuen.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (leaves 82-89).
Abstracts in English and Chinese.
Chapter Chapter 1 --- Introduction --- p.1
Chapter Chapter 2 --- Review of Linearization Techniques --- p.4
Chapter 2.1 --- Feedforward --- p.5
Chapter 2.2 --- Feedback --- p.7
Chapter 2.3 --- Predistortion --- p.10
Chapter Chapter 3 --- The Volterra Series Method for Nonlinear Analysis --- p.12
Chapter 3.1 --- Volterra Series Method --- p.13
Chapter 3.2 --- Nonlinear Transfer Function --- p.14
Chapter 3.3 --- Weakly Nonlinear Approximation --- p.18
Chapter 3.4 --- Nonlinear Modeling --- p.19
Chapter 3.5 --- Determination of Nonlinear Transfer Function --- p.22
Chapter Chapter 4 --- Manifestation of Nonlinear Behavior --- p.25
Chapter 4.1 --- Two-Tone Volterra Series Analysis --- p.25
Chapter 4.2 --- Harmonic Distortion --- p.28
Chapter 4.3 --- AM/AM and AM/PM --- p.29
Chapter 4.4 --- Intermodulation Distortion --- p.31
Chapter Chapter 5 --- The Generalized Baseband Signal Injection Method --- p.33
Chapter 5.1 --- Generalized Baseband Signal Injection Method (GM) --- p.34
Chapter 5.2 --- Application of GM to Predistorter-Amplifier Linearization --- p.38
Chapter 5.2.1 --- Case 1: Standalone Amplifier without Injection --- p.40
Chapter 5.2.2 --- Case 2: Injection to Amplifier Only --- p.41
Chapter 5.2.3 --- Case 3: Injection to Diode Predistorter Only --- p.41
Chapter 5.2.4 --- Case 4: Injection to Both Diode Predistorter and Amplifier --- p.42
Chapter 5.3 --- Application of GM to Multi-Stage Amplifier Linearization --- p.43
Chapter 5.3.1 --- Case 1: Amplifying System with No Signal Injection --- p.46
Chapter 5.3.2 --- Case 2: Amplifying System with Single Injection Point --- p.47
Chapter 5.3.3 --- Case 3: Amplifying System with Two Injection Points --- p.48
Chapter Chapter 6 --- Experimental Setup and Measurements --- p.50
Chapter 6.1 --- Experimental Setup --- p.51
Chapter 6.1.1 --- Diode Predistorter --- p.51
Chapter 6.1.2 --- Small Signal Amplifier --- p.54
Chapter 6.1.3 --- Medium Power Amplifier --- p.58
Chapter 6.1.4 --- Baseband Signal Generation Circuit --- p.61
Chapter 6.1.5 --- Baseband Amplifiers --- p.63
Chapter 6.2 --- Linearization of Amplifier with Predistortion Circuitry --- p.65
Chapter 6.2.1 --- Two-Tone Test --- p.65
Chapter 6.2.2 --- Vector Signal Test --- p.68
Chapter 6.2.3 --- Dynamic Range Evaluation --- p.70
Chapter 6.3 --- Linearization of Multi-Stage Amplifying System --- p.71
Chapter 6.3.1 --- Determination of Transfer and Gain Coefficients --- p.71
Chapter 6.3.2 --- Two-Tone Test --- p.74
Chapter 6.3.3 --- Vector Signal Test --- p.77
Chapter 6.3.4 --- Dynamic Range Evaluation --- p.79
Chapter Chapter 7 --- Conclusion and Future Work --- p.80
References --- p.82
Author's Publications --- p.90

碩士
國立中央大學
通訊工程學系
104
It is well known that Orthogonal Frequency Division Multiplexing (OFDM) has become indispensable in modern wireless communications because of high frequency efficiency and high transmission stability in multi-path channel environments. However, OFDM has an inherent characteristic of high Peak-to-Average Power Ratio (PAPR) subject to nonlinear distortion of a power amplifier, leading to the phenomenon of spectral regrowth for modulated signals such that the adjacent communication channels are interfered. Taking into account the memory problem in wideband systems, this thesis studied a new pre-distortion scheme for the power amplifier. From previous researches in the literature, there have been many predistorter’s models considering to compensate for the nonlinearity effect of memory in a power amplifier. In our framework, we first establish the Weiner model for characterizing the power amplifier and then use the Hammerstein model for the predistorter along with the baseband Simplicial Canonical Piecewise Linear (SCPWL) function for nonlinear modeling. Compared with previous predistorting methods, the proposed predistorter is easier to reach the required performance by adjusting the number of segments of the SCPWL function. For the indirect predistortion architecture, we use the Recursive Prediction Error Method (RPEM) for adaptive estimation of the parameters of the proposed predistorter, which can achieve a satisfying system performance and fast convergence speed for better linearization.

碩士
國立中央大學
通訊工程學系
106
It is well known that Orthogonal Frequency Division Multiplexing (OFDM) has become indispensable in modern wireless communications because of high frequency efficiency and high transmission stability in multi-path channel environments. However, OFDM has an inherent characteristic of high Peak-to-Average Power Ratio(PAPR) subject to nonlinear distortion of a power amplifier, leading to the phenomenon of spectral regrowth for modulated signals such that the adjacent communication channels are interfered. Taking into account the memory problem in wideband systems, this thesis studied a new predistortion scheme for the power amplifier. From previous researches in the literature, there have been many predistorter’s models considering to compensate for the nonlinearity effect of a power amplifier. In our framework, we first establish the Saleh model for characterizing the power amplifier followed by a LTI model and then use the Memory polynomial model for the predistorter. Compared with previous predistortion methods, the proposed predistorter is easier to reach the required performance with a with a new chaotic particle swarm optimization(NCPSO) method at a satisfying convergence rate.

In this thesis, investigation of robust stability properties for certain nonlinear systems via exact linearization is presented, and guidelines for designing a robust controller are provided which guarantee the system stability under certain system perturbations, disturbances, and performance requirements. Comparisons of robustness analysis and design between linear and nonlinear feedback systems are presented. The robust stability conditions for nonlinear feedback systems when the uncertainties occur at various points in the original nonlinear system are obtained from Lyapunov stability analysis. Using conic sector analysis to analyze the nonlinear robustness properties, time domain constraints on nonlinearity of a system is related to frequency domain constraints on the transformed linear system. Gain margins for gain perturbations of the control effectiveness in the nonlinear system are developed. The bounds on the perturbations which the feedback system can tolerate are given as robust stability conditions.

碩士
國立臺灣科技大學
營建工程系
103
To improve the complication and time-consumimg of the RC structures in nonlinear dynamic analysis, through SDOF and spine model to simulate nonlinear dynamic analysis, and replace the traditional equivalent linearization method that must be repeated to estimate the maximum displacement of the nonlinear structures. This study can estimated the maximum displacement without iterative calculation, for Taiwan’s seismic design code and structural dynamics concern, established an equivalent linearization method of Taiwan as well as using pushover analysis estimated the story displacement and drift ratio；In order to increase the accuracy and feasibility, also presented the modify method with regard to the error between nonlinear dynamic analysis and equivalent linearization method of the short period and the long period region.This study can efficiently converted the design seismic response spectrum to ductility demand spectrum, to provide engineers the displacement and ductility demand of the structures.

碩士
國立臺灣科技大學
營建工程系
106
When reinforced concrete structures are subjected to earthquake ground motion, the structural system is likely to develop some damage. Many researchers had proposed damage index for the purpose of quantifying the damage potential developed during seismic event. In general the damage potential could be determined by the combination of maximum deformation response and the hysteretic energy dissipation. In this study, an equivalent linearization method to estimate the maximum deformation of single-degree-of-freedom system is used to develop the ductility demand and damage spectra. The result from nonlinear dynamic analysis with total 348 ground motion records is used to investigate the uncertainty of the approximation method under various site conditions. Since equivalent linearization method is relatively easy to use, the development of the ductility demand spectra can be used as a tool by the engineers in specifying the design strength or ductility capacity level. Additionally, cumulative effect of cyclic loading and the aftershock effect are also discussed in this study.

The tail-equivalent linearization method (TELM) is used to investigate the stationary response of a system having a highly asymmetric hysteretic behavior and subjected to a discretized white-noise excitation. The equivalent linear system is defined by equating its tail probability with the first-order approximation of the tail probability of the nonlinear response. The equivalent linear system is determined in a non-parametric form in terms of its impulse response function, which depends on the response threshold of interest. The method is able to capture the non-Gaussian and asymmetric distribution of both the point-in-time response and the extreme response over a time interval (the first-passage probability) for large thresholds (small exceedance probabilities), which are of interest in reliability analysis.

碩士
國立臺灣科技大學
營建工程系
107
Generally, earthquakes recorded within the near-fault characteristic are qualitatively quite different from the usual far-fault earthquake. Because of the unique characteristics of near-fault earthquake, many researchers have developed several performance-based seismic design in order to quantify the damage potential caused by near-fault earthquake. Based on the Taiwan seismic design code and the past research conducted by Okano and Miyamoto [7], this study proposes the modified equivalent linearization method (MELM) of a SDOF system for a low-rise and mid-rise reinforced concrete (RC) building structure subjected to near-fault earthquake. Actually for high-rise building, the engineer needs to do the dynamic analysis. However, for low-rise and mid-rise building in Taiwan actually is not necessary doing the dynamic analysis. Therefore, the purpose of this study is to propose the equation which can help the engineer to estimate the maximum deformation of the building subjected to earthquake so that they do not need to do the dynamic analysis. In addition, for a building structure designed based on the code-suggested static design procedure cannot be used to investigate the damage state of a specified building under the earthquake. Therefore, the constant-damage ductility demand spectrum (CDDDS) for a reinforced concrete (RC) building that corresponds to a specified reliability is developed in this study based on the study conducted by Park and Ang [1].

A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the method through applications to non-linear oscillators, we also use the Girsanov transformation of measures to correct the truncation errors in lower order discretizations. In order to achieve efficiency in the computation of response statistics via Monte Carlo simulation, we propose in Chapter 4 a weak variance reduction strategy such that the ensemble size is significantly reduced without seriously affecting the accuracy of the predicted expectations of any smooth function of the response vector. The basis of the variance reduction strategy is to appropriately augment the governing system equations and then weakly replace the associated stochastic forcing functions through variance-reduced functions. In the process, the additional computational cost due to system augmentation is generally far less besides the accrued advantages due to a drastically reduced ensemble size. The variance reduction scheme is illustrated through applications to several non-linear oscillators, including a 3-DOF system. Finally, in Chapter 5, we exploit the explicit forms of the LTL techniques for state and parameters estimations of non-linear oscillators of engineering interest using a novel derivative-free EKF and a 2-EKF. In the derivative-free EKF, we use one-term, Euler and Newmark replacements for linearizations of the non-linear drift terms. In the 2-EKF, we use bias terms to account for errors due to lower order linearization and unmodelled dynamics in the mathematical model. Numerical studies establish the relative advantages of EKF-DLL as well as 2-EKF over the conventional forms of EKF. The thesis is concluded in Chapter 6 with an overall summary of the contributions made and suggestions for future research.

A main thrust of this thesis is to develop and explore linearization-based numeric-analytic integration techniques in the context of stochastically driven nonlinear oscillators of relevance in structural dynamics. Unfortunately, unlike the case of deterministic oscillators, available numerical or numeric-analytic integration schemes for stochastically driven oscillators, often modelled through stochastic differential equations (SDE-s), have significantly poorer numerical accuracy. These schemes are generally derived through stochastic Taylor expansions and the limited accuracy results from difficulties in evaluating the multiple stochastic integrals. We propose a few higher-order methods based on the stochastic version of transversal linearization and another method of linearizing the nonlinear drift field based on a Girsanov change of measures. When these schemes are implemented within a Monte Carlo framework for computing the response statistics, one typically needs repeated simulations over a large ensemble. The statistical error due to the finiteness of the ensemble (of size N, say)is of order 1/√N, which implies a rather slow convergence as N→∞. Given the prohibitively large computational cost as N increases, a variance reduction strategy that enables computing accurate response statistics for small N is considered useful. This leads us to propose a weak variance reduction strategy. Finally, we use the explicit derivative-free linearization techniques for state and parameter estimations for structural systems using the extended Kalman filter (EKF). A two-stage version of the EKF (2-EKF) is also proposed so as to account for errors due to linearization and unmodelled dynamics. In Chapter 2, we develop higher order locally transversal linearization (LTL) techniques for strong and weak solutions of stochastically driven nonlinear oscillators. For developing the higher-order methods, we expand the non-linear drift and multiplicative diffusion fields based on backward Euler and Newmark expansions while simultaneously satisfying the original vector field at the forward time instant where we intend to find the discretized solution. Since the non-linear vector fields are conditioned on the solution we wish to determine, the methods are implicit. We also report explicit versions of such linearization schemes via simple modifications. Local error estimates are provided for weak solutions. Weak linearized solutions enable faster computation vis-à-vis their strong counterparts. In Chapter 3, we propose another weak linearization method for non-linear oscillators under stochastic excitations based on Girsanov transformation of measures. Here, the non-linear drift vector is appropriately linearized such that the resulting SDE is analytically solvable. In order to account for the error in replacing of non-linear drift terms, the linearized solutions are multiplied by scalar weighting function. The weighting function is the solution of a scalar SDE(i.e.,Radon-Nikodym derivative). Apart from numerically illustrating the method through applications to non-linear oscillators, we also use the Girsanov transformation of measures to correct the truncation errors in lower order discretizations. In order to achieve efficiency in the computation of response statistics via Monte Carlo simulation, we propose in Chapter 4 a weak variance reduction strategy such that the ensemble size is significantly reduced without seriously affecting the accuracy of the predicted expectations of any smooth function of the response vector. The basis of the variance reduction strategy is to appropriately augment the governing system equations and then weakly replace the associated stochastic forcing functions through variance-reduced functions. In the process, the additional computational cost due to system augmentation is generally far less besides the accrued advantages due to a drastically reduced ensemble size. The variance reduction scheme is illustrated through applications to several non-linear oscillators, including a 3-DOF system. Finally, in Chapter 5, we exploit the explicit forms of the LTL techniques for state and parameters estimations of non-linear oscillators of engineering interest using a novel derivative-free EKF and a 2-EKF. In the derivative-free EKF, we use one-term, Euler and Newmark replacements for linearizations of the non-linear drift terms. In the 2-EKF, we use bias terms to account for errors due to lower order linearization and unmodelled dynamics in the mathematical model. Numerical studies establish the relative advantages of EKF-DLL as well as 2-EKF over the conventional forms of EKF. The thesis is concluded in Chapter 6 with an overall summary of the contributions made and suggestions for future research.

This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes. In Chapter 4, we explore the possibility of unscented transformation on Gaussian random variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence. The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications. The thesis is finally wound up in Chapter 7 by summarizing these developments and briefly outlining the future research directions

This thesis essentially deals with the development and numerical explorations of a few improved Monte Carlo filters for nonlinear dynamical systems with a view to estimating the associated states and parameters (i.e. the hidden states appearing in the system or process model) based on the available noisy partial observations. The hidden states are characterized, subject to modelling errors, by the weak solutions of the process model, which is typically in the form of a system of stochastic ordinary differential equations (SDEs). The unknown system parameters, when included as pseudo-states within the process model, are made to evolve as Wiener processes. The observations may also be modelled by a set of measurement SDEs or, when collected at discrete time instants, their temporally discretized maps. The proposed Monte Carlo filters aim at achieving robustness (i.e. insensitivity to variations in the noise parameters) and higher accuracy in the estimates whilst retaining the important feature of applicability to large dimensional nonlinear filtering problems. The thesis begins with a brief review of the literature in Chapter 1. The first development, reported in Chapter 2, is that of a nearly exact, semi-analytical, weak and explicit linearization scheme called Girsanov Corrected Linearization Method (GCLM) for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories whilst weakly applying the Girsanov correction (the Radon- Nikodym derivative) for the linearization errors. Through their numeric implementations for a few workhorse nonlinear oscillators, the proposed variants of the scheme are shown to exhibit significantly higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own. The above scheme for linearization correction is exploited and extended in Chapter 3, wherein novel variations within a particle filtering algorithm are proposed to weakly correct for the linearization or integration errors that occur while numerically propagating the process dynamics. Specifically, the correction for linearization, provided by the likelihood or the Radon-Nikodym derivative, is incorporated in two steps. Once the likelihood, an exponential martingale, is split into a product of two factors, correction owing to the first factor is implemented via rejection sampling in the first step. The second factor, being directly computable, is accounted for via two schemes, one employing resampling and the other, a gain-weighted innovation term added to the drift field of the process SDE thereby overcoming excessive sample dispersion by resampling. The proposed strategies, employed as add-ons to existing particle filters, the bootstrap and auxiliary SIR filters in this work, are found to non-trivially improve the convergence and accuracy of the estimates and also yield reduced mean square errors of such estimates visà-vis those obtained through the parent filtering schemes. In Chapter 4, we explore the possibility of unscented transformation on Gaussian random variables, as employed within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems. We propose in Chapter 5 an iterated gain-based particle filter that is consistent with the form of the nonlinear filtering (Kushner-Stratonovich) equation in our attempt to treat larger dimensional filtering problems with enhanced estimation accuracy. A crucial aspect of the proposed filtering set-up is that it retains the simplicity of implementation of the ensemble Kalman filter (EnKF). The numerical results obtained via EnKF-like simulations with or without a reduced-rank unscented transformation also indicate substantively improved filter convergence. The final contribution, reported in Chapter 6, is an iterative, gain-based filter bank incorporating an artificial diffusion parameter and may be viewed as an extension of the iterative filter in Chapter 5. While the filter bank helps in exploring the phase space of the state variables better, the iterative strategy based on the artificial diffusion parameter, which is lowered to zero over successive iterations, helps improve the mixing property of the associated iterative update kernels and these are aspects that gather importance for highly nonlinear filtering problems, including those involving significant initial mismatch of the process states and the measured ones. Numerical evidence of remarkably enhanced filter performance is exemplified by target tracking and structural health assessment applications. The thesis is finally wound up in Chapter 7 by summarizing these developments and briefly outlining the future research directions

In this dissertation, we propose a set of computationally efficient methods based on approximating/representing nonlinear processes by linear ones, so-called linearization. Firstly, a linearization method is introduced for estimating the multiple frequencies in sinusoidal processes. It utilizes a regularized autoregressive (AR) approximation, which can be regarded as a "large p - small n" approach in a time series context. An appealing property of regularized AR is that it avoids a model selection step and allows for an efficient updating of the frequency estimates whenever new observations are obtained. The theoretical analysis shows that the regularized AR frequency estimates are consistent and asymptotically normally distributed. Secondly, a sieve bootstrap scheme is proposed using the linear representation of generalized autoregressive conditional heteroscedastic (GARCH) models to construct prediction intervals (PIs) for the returns and volatilities. Our method is simple, fast and distribution-free, while providing sharp and well-calibrated PIs. A similar linear bootstrap scheme can also be used for diagnostic testing. Thirdly, we introduce a robust lagrange multiplier (LM) test, which utilizes either the bootstrap or permutation procedure to obtain critical values, for detecting GARCH effects. We justify that both bootstrap and permutation LM tests are consistent. Intensive numerical studies indicate that the proposed resampling algorithms significantly improve the size and power of the LM test in both skewed and heavy-tailed processes. Moreover, fourthly, we introduce a nonparametric trend test in the presence of GARCH effects (NT-GARCH) based on heteroscedastic ANOVA. Our empirical evidence show that NT-GARCH can effectively detect non-monotonic trends under GARCH, especially in the presence of irregular seasonal components. We suggest to apply the bootstrap procedure for both selecting the window length and finding critical values. The newly proposed methods are illustrated by applications to astronomical data, to foreign currency exchange rates as well as to water and air pollution data. Finally, the dissertation is concluded by an outlook on further extensions of linearization methods, e.g., in model order selection and change point detection.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

碩士
國立臺北科技大學
商業自動化與管理研究所
95
Many problems in management and engineering are constructed as nonlinear programming models. Various nonlinear programming techniques have been proposed in the past. Since the nonlinear programming models contain a lot of local optimal solutions, current methods have difficulty to obtain a globally optimal solution. This study presents three deterministic global optimization methods for nonlinear programming problems. The three methods guarantee to find a global optimum within a tolerable error. Moreover, an optimization system is developed to construct the mathematical model according to the three optimization methods automatically. Finally, practical examples are presented to compare the efficiency and properties of the optimization approaches.