Dissertations / Theses on the topic 'Fuzzy- stochastic structural analysis'

The Presented Thesis is focused on exploitation of stochastic cyclical networks in project management during project planning. Particularly, it is focused on the GERT method, which enables to carry out both the probability analysis and the time analysis of projects with stochastic structure. We deal primarily with analysis of such networks where cyclical activities occur. As an integral part of the Thesis, derivation of simplified computing procedures for cyclical activities is included. We extend the possibilities of the GERT method with stochastic evaluation of time duration of activities using the fuzzy GERT method. This fuzzy GERT method is applied on the real project and its results are compared to results of Monte Carlo simulation.

Mit der Fuzzy-Stochastischen Finite-Elemente-Methode (FSFEM) kann die nachgewiesene stochastische und nichtstochastische Datenunschärfe des stahlbewehrten Altbetons und des Textilbeton bei der Strukturanalyse berücksichtigt werden. Die für die deterministische Analyse textilverstärkter Tragwerke auf der Basis des Multi-Referenzebenen-Modells (MRM) entwickelten finiten MRM-Elemente wurden zu FSMRM-Elementen weiterentwickelt. Das Stoffmodell des mit AR-Glas bewehrten Feinbetons wurde für textile Gelege aus Carbon erweitert. Die entwickelten Modelle und Algorithmen werden zur fuzzystochastischen Tragwerksanalyse textilverstärkter Tragwerke eingesetzt.

Bibliography: p. 113-123.
This thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs without requiring major code development. These routines are implemented in the general purpose finite element program ABAQUS through its user element subroutine facility and two probabilistic finite elements are developed: a three-dimensional beam element limited to linear material behaviour and a two-dimensional plane element involving elastic-plastic material behaviour. The plane element incorporates plane strain, plane stress and axisymmetric formulations. The numerical accuracy and robustness of the routines are verified and application of the probabilistic finite element method is illustrated in two case studies, one involving a four-story, two-bay frame structure, the other a reactor pressure vessel nozzle. The probabilistic finite element routines developed in this thesis integrate point estimate methods and mean value first order methods within the same program. Both methods require a systematic sequence involving the perturbation of the random parameters to be evaluated, although the perturbation sequence of the methods differ. It is shown that computer-time saving techniques such as Taylor series and iterative perturbation schemes, developed for mean value based methods, can also be used to solve point estimate method problems. These efficient techniques are limited to linear problems; nonlinear problems must use full perturbation schemes. Finally, it is shown that all these probabilistic methods and perturbation schemes can be integrated within one program and can follow many of the existing deterministic program structures and subroutines. An overall strategy for converting deterministic finite element programs to probabilistic finite element programs is outlined.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.
Includes bibliographical references (leaves 113-116). Also available in electronic version. Access restricted to campus users.

The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influ­ence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of sys­tems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assess­ment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understand­ing phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with diffi­culties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further com­pounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the for­mulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochas­tic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is consid­ered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the pre­vious chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteris­tics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinc­tive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical so­lutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been ac­cepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

Orientador: Jose Roberto de França Arruda
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-08-05T10:01:28Z (GMT). No. of bitstreams: 1 Nunes_RonaldoFernandes_D.pdf: 2368458 bytes, checksum: 01da7061fcacf61682f9aa00dceb6837 (MD5) Previous issue date: 2005
Resumo: Neste trabalho, o problema da análise dinâmica de estruturas em médias freqüências é abordado. Em geral, métodos numéricos tais como elementos finitos e elementos de contorno não são apropriados para tratar estes casos. As principais razões são a necessidade do refinamento das malhas com o aumento da freqüência e o cálculo da influência dos parâmetros incertos, cujo efeito em particular, para médias e altas freqüências, tende a ser significativo. O problema do refinamento do modelo pode ser superado através de métodos semi-analíticos, como por exemplo, o método do elemento espectral. Em relação à simulação dos sistemas com parâmetros de entrada incertos, métodos baseados em conjuntos nebulosos e métodos probabilísticos são adotados. Nesta tese, uma proposta combinando o método do elemento espectral com conjuntos nebulosos é conduzida. O principal foco deste trabalho é apresentar uma nova abordagem para o problema em médias freqüências. Neste contexto, funções de resposta em freqüência são adotadas para representar o efeito dos parâmetros de entrada não determinísticos na resposta dinâmica de estruturas. Para ilustrar o procedimento proposto, exemplos numéricos são tratados, como o caso simples de uma placa retangular reforçada com vigas e também o caso de uma estrutura do tipo pórtico
Abstract: It is well-known that, in the mid-frequency range, numerical methods such as finite and boundary elements are not suitable for structural dynamic analysis. One of the reasons is the fine mesh resolution required to accurately model the physical problem, leading to large computational models. The other reason is associated with the difficulty in estimating the response statistics for system parameter variations. The mesh refinement problem can be addressed using semi-analytical methods, such as the spectral element method. However, in general, these methods are very limited with respect to the geometry and boundary conditions that can be treated. With respect to parameter variation, the simulation of systems with uncertain parameters has in the past been addressed with different techniques, such as finite elements applied to stochastic problems and fuzzy set based methods. In this thesis, the spectral element method is combined with a special implementation of a fuzzy set based method that avoids the well-know effect of overestimation in interval computations. In this regard, some efficient alternatives, such as the transformation method and the sparse grids approach are proposed. In this work, the main goal is to provide alternatives to address dynamic problems under uncertainty in the mid-frequency range. In this context, envelopes for frequency response functions are used to represent the effect of non-deterministic input parameters in the dynamic response of structures. To illustrate he proposed procedure, numerical examples are treated, such as a simple rectangular plate reinforced with beams and a frame-type model
Doutorado
Mecanica dos Sólidos e Projeto Mecanico
Doutor em Engenharia Mecânica

Corrosion of reinforcing bars is the major cause of deterioration of reinforced concrete (RC) structures in North America, Europe, the Middle East, and many coastal regions around the world. This deterioration leads to a loss of serviceability and functionality and ultimately affects the structural safety. The objective of this research is to formulate and implement a general stochastic finite element analysis (SFEA) framework for the time-dependent reliability analysis of RC beams with corroding flexural reinforcement. The framework is based on the integration of nonlinear finite element and reliability analyses through an iterative response surface methodology (RSM). Corrosion-induced damage is modelled through the combined effects of gradual loss of the cross-sectional area of the steel reinforcement and the reduction bond between steel and concrete for increasing levels of corrosion. Uncertainties in corrosion rate, material properties, and imposed actions are modelled as random variables. Effective implementation of the framework is achieved by the coupling of commercial finite element and reliability software. Application of the software is demonstrated through a case study of a simply-supported RC girder with tension reinforcement subjected to the effects of uniform (general) corrosion, in which two limit states are considered: (i) a deflection serviceability limit state and (ii) flexural strength ultimate limit state. The results of the case study show that general corrosion leads to a very significant decrease in the reliability of the RC beam both in terms of flexural strength and maximum deflections. The loss of strength and serviceability was shown to be predominantly caused by the loss of bond strength, whereas the gradual reduction of the cross-sectional area of tension reinforcement was found to be insignificant. The load-deflection response is also significantly affected by the deterioration of bond strength (flexural strength and stiffness). The probability of failure at the end of service life, due to the effects of uniform corrosion-induced degradation, is observed to be approximately an order of magnitude higher than in the absence of corrosion. Furthermore, the results suggest that flexural resistance of corroded RC beams is controlled by the anchorage (bond) of the bars and not by the yielding of fully bonded tensile reinforcement at failure. This is significant since the end regions can be severely corroded due to chloride, moisture, and oxygen access at connections and expansion joints. The research strongly suggests that bond damage must be considered in the assessment of the time-dependent reliability of RC beams subjected to general corrosion.

Thesis (MScEng)-- Stellenbosch University, 2013.
ENGLISH ABSTRACT: Most of the parameters involved in the design and analysis of structures are of stochastic nature. This is, therefore, of paramount importance to be able to perform a fully stochastic analysis of structures both in component and system level to take into account the uncertainties involved in structural analysis and design. To the contrary, in practice, the (computerised) analysis of structures is based on a deterministic analysis which fails to address the randomness of design and analysis parameters. This means that an investigation on the algorithmic methodologies for a component and system reliability analysis can help pave the way towards the implementation of fully stochastic analysis of structures in a computer environment. This study is focused on algorithm development for component and system reliability analysis based on the various proposed methodologies. Truss structures were selected for this purpose due to their simplicity as well as their wide use in the industry. Nevertheless, the algorithms developed in this study can be used for other types of structures such as moment-resisting frames with some simple modi cations. For a component level reliability analysis of structures different methods such as First Order Reliability Methods (FORM) and simulation methods are proposed. However, implementation of these methods for the statistically indeterminate structures is complex due to the implicit relation between the response of the structural system and the load effect. As a result, the algorithm developed for the purpose of component reliability analysis should be based on the concepts of Stochastic Finite Element Methods (SFEM) where a proper link between the finite element analysis of the structure and the reliability analysis methodology is ensured. In this study various algorithms are developed based on the FORM method, Monte Carlo simulation, and the Response Surface Method (RSM). Using the FORM method, two methodologies are considered: one is based on the development of a finite element code where required alterations are made to the FEM code and the other is based on the usage of a commercial FEM package. Different simulation methods are also implemented: Direct Monte Carlo Simulation (DMCS), Latin Hypercube Sampling Monte Carlo (LHCSMC), and Updated Latin Hypercube Sampling Monte Carlo (ULHCSMC). Moreover, RSM is used together with simulation methods. Throughout the thesis, the effciency of these methods was investigated. A Fully Stochastic Finite Element Method (FSFEM) with alterations to the finite element code seems the fastest approach since the linking between the FEM package and reliability analysis is avoided. Simulation methods can also be effectively used for the reliability evaluation where ULHCSMC seemed to be the most efficient method followed by LHCSMC and DMCS. The response surface method is the least straight forward method for an algorithmic component reliability analysis; however, it is useful for the system reliability evaluation. For a system level reliability analysis two methods were considered: the ß-unzipping method and the branch and bound method. The ß-unzipping method is based on a level-wise system reliability evaluation where the structure is modelled at different damaged levels according to its degree of redundancy. In each level, the so-called unzipping intervals are defined for the identification of the critical elements. The branch and bound method is based on the identification of different failure paths of the structure by the expansion of the structural failure tree. The evaluation of the damaged states for both of the methods is the same. Furthermore, both of the methods lead to the development of a parallel-series model for the structural system. The only difference between the two methods is in the search approach used for the failure sequence identification. It was shown that the ß-unzipping method provides a better algorithmic approach for evaluating the system reliability compared to the branch and bound method. Nevertheless, the branch and bound method is a more robust method in the identification of structural failure sequences. One possible way to increase the efficiency of the ß-unzipping method is to define bigger unzipping intervals in each level which can be possible through a computerised analysis. For such an analysis four major modules are required: a general intact structure module, a damaged structure module, a reliability analysis module, and a system reliability module. In this thesis different computer programs were developed for both system and component reliability analysis based on the developed algorithms. The computer programs are presented in the appendices of the thesis.
AFRIKAANSE OPSOMMING: Meeste van die veranderlikes betrokke by die ontwerp en analise van strukture is stogasties in hul aard. Om die onsekerhede betrokke in ontwerp en analise in ag te neem is dit dus van groot belang om 'n ten volle stogastiese analise te kan uitvoer op beide komponent asook stelsel vlak. In teenstelling hiermee is die gerekenariseerde analise van strukture in praktyk gebaseer op deterministiese analise wat nie suksesvol is om die stogastiese aard van ontwerp veranderlikes in ag te neem nie. Dit beteken dat die ondersoek na die algoritmiese metodiek vir komponent en stelsel betroubaarheid analise kan help om die weg te baan na die implementering van ten volle rekenaarmatige stogastiese analise van strukture. Di e studie se fokus is op die ontwikkeling van algoritmes vir komponent en stelsel betroubaarheid analise soos gegrond op verskeie voorgestelde metodes. Vakwerk strukture is gekies vir die doeleinde as gevolg van hulle eenvoud asook hulle wydverspreide gebruik in industrie. Die algoritmes wat in die studie ontwikkel is kan nietemin ook vir ander tipes strukture soos moment-vaste raamwerke gebruik word, gegewe eenvoudige aanpassings. Vir 'n komponent vlak betroubaarheid analise van strukture word verskeie metodes soos die "First Order Reliability Methods" (FORM) en simulasie metodes voorgestel. Die implementering van die metodes vir staties onbepaalbare strukture is ingewikkeld as gevolg van die implisiete verband tussen die gedrag van die struktuur stelsel en die las effek. As 'n gevolg, moet die algoritme wat ontwikkel word vir die doel van komponent betroubaarheid analise gebaseer word op die konsepte van stogastiese eindige element metodes ("SFEM") waar 'n duidelike verband tussen die eindige element analise van die struktuur en die betroubaarheid analise verseker is. In hierdie studie word verskeie algoritmes ontwikkel wat gebaseer is op die FORM metode, Monte Carlo simulasie, en die sogenaamde "Response Surface Method" (RSM). Vir die gebruik van die FORM metode word twee verdere metodologieë ondersoek: een gebaseer op die ontwikkeling van 'n eindige element kode waar nodige verandering aan die eindige element kode self gemaak word en die ander waar 'n kommersiële eindige element pakket gebruik word. Verskillende simulasie metodes word ook geïmplimenteer naamlik Direkte Monte Carlo Simulasie (DMCS), "Latin Hypercube Sampling Monte Carlo" (LHCSMC) en sogenaamde "Updated Latin Hypercube Sampling Monte Carlo" (ULHCSMC). Verder, word RSM tesame met die simulasie metodes gebruik. In die tesis word die doeltreffendheid van die bostaande metodes deurgaans ondersoek. 'n Ten volle stogastiese eindige element metode ("FSFEM") met verandering aan die eindige element kode blyk die vinnigste benadering te wees omdat die koppeling tussen die eindige element metode pakket en die betroubaarheid analise verhoed word. Simulasie metodes kan ook effektief aangewend word vir die betroubaarheid evaluasie waar ULHCSMC as die mees doeltre end voorgekom het, gevolg deur LHCSMC en DMCS. The RSM metode is die mees komplekse metode vir algoritmiese komponent betroubaarheid analise. Die metode is egter nuttig vir sisteem betroubaarheid analise. Vir sisteem-vlak betroubaarheid analise is twee metodes oorweeg naamlik die "ß-unzipping" metode and die "branch-and-bound" metode. Die "ß-unzipping" metode is gebaseer op 'n sisteem-vlak betroubaarheid ontleding waar die struktuur op verskillende skade vlakke gemodelleer word soos toepaslik vir die hoeveelheid addisionele las paaie. In elke vlak word die sogenaamde "unzipping" intervalle gedefinieer vir die identifikasie van die kritiese elemente. Die "branch-and-bound" metode is gebaseer op die identifikasie van verskillende faling roetes van die struktuur deur uitbreiding van die falingsboom. The ondersoek van die skade toestande vir beide metodes is dieselfde. Verder kan beide metodes lei tot die ontwikkeling van 'n parallelserie model van die strukturele stelsel. Die enigste verskil tussen die twee metodes is in die soek-benadering vir die uitkenning van falingsmodus volgorde. Dit word getoon dat die "ß-unzipping" metode 'n beter algoritmiese benadering is vir die ontleding van sisteem betroubaarheid vergeleke met die "branch-and-bound" metode. Die "branch-and- bound" metode word nietemin as 'n meer robuuste metode vir die uitkenning van die falings volgorde beskou. Een moontlike manier om die doeltre endheid van die "ß-unzipping" metode te verhoog is om groter "unzipping" intervalle te gebruik, wat moontlik is vir rekenaarmatige analise. Vir so 'n analise word vier hoof modules benodig naamlik 'n algemene heel-struktuur module, 'n beskadigde-struktuur module, 'n betroubaarheid analise module en 'n sisteem betroubaarheid analise module. In die tesis word verskillende rekenaar programme ontwikkel vir beide sisteem en komponent betroubaarheid analise. Die rekenaar programme word in die aanhangsels van die tesis aangebied.

The paper studies structural credit risk models with incomplete information of the asset value. It is shown that the pricing of typical corporate securities such as equity, corporate bonds or CDSs leads to a nonlinear filtering problem. This problem cannot be tackled with standard techniques as the default time does not have an intensity under full information. We therefore transform the problem to a standard filtering problem for a stopped diffusion process. This problem is analyzed via SPDE results from the filtering literature. In particular we are able to characterize the default intensity under incomplete information in terms of the conditional density of the asset value process. Moreover, we give an explicit description of the dynamics of corporate security prices. Finally, we explain how the model can be applied to the pricing of bond and equity options and we present results from a number of numerical experiments.

Il presente elaborato affronta il problema del rilevamento dei danni strutturali nell’ambito dello Structural Health Monitoring (SHM) attraverso l’identificazione delle caratteristiche dinamiche delle strutture e con il solo utilizzo di vibrazioni ambientali. Questa procedura pertiene all’Operational Modal Analysis (OMA), campo dell’ingegneria che, tenendo conto della sola risposta del sistema senza conoscerne l’input, cattura i segnali nel dominio del tempo o della frequenza e identifica i parametri modali del sistema: frequenze naturali, indici di smorzamento e forme modali. Il successo di ogni metodo OMA dipende dalle caratteristiche dei segnali acquisiti, come la durata della loro registrazione o la frequenza di campionamento, e dal tipo di sistema di rilevamento, ad esempio la Wireless Sensor Network (WSN), rete meno costosa e più facile da realizzare rispetto a quella cablata, ma che registra un Time Synchronization Error (TSE) tra i clock dei suoi nodi sensore. Tra i metodi OMA, le tecniche Stochastic Subspace Identification (SSI) sono considerate tra le più potenti e affidabili nel dominio del tempo. Il nucleo di questo lavoro è la presentazione dei due approcci SSI, il Covariance-driven e il Data-driven, e il confronto tra le loro prestazioni, al fine di indagarne vantaggi e svantaggi anche attraverso la loro applicazione pratica. Viene studiata, in particolare, l’influenza della durata del segnale acquisito e dell’errore di sincronizzazione sulla precisione del calcolo delle proprietà dinamiche stimate con gli algoritmi SSI, che vengono poi confrontate con quelle ottenute grazie alla tecnica Frequency Domain Decomposition (FDD). Dai risultati numerici risulta che per ottenere una buona stima dei parametri modali si può ricorrere anche ad un segnale di breve durata e che il TSE ha un impatto negativo sul calcolo delle forme modali.

Detecção de dano em estruturas de engenharia de grandes dimensões através da análise de suas características dinâmicas envolve diversos campos de estudo. O primeiro deles trata da identificação dos parâmetros modais da estrutura, uma vez que executar testes de vibração livre em tais estruturas não é uma tarefa simples, necessita-se de um método robusto que seja capaz de identificar os parâmetros modais dessa estrutura a ações ambientais, campo esse chamado de análise modal operacional. Este trabalho trata do problema de detecção de dano em estruturas que possam ser representadas através de modelos em pórticos planos e vigas e que estejam submetidos à ação de vibrações ambientais. A localização do dano é determinada através de um algoritmo de otimização conhecido como Backtracking Search Algorithm (BSA) fazendo uso de uma função objetivo que utiliza as frequências naturais e modos de vibração identificados da estrutura. Simulações e testes são feitos a fim de verificar a concordância da metodologia para ambos os casos. Para as simulações, são utilizados casos mais gerais de carregamentos dinâmicos, e dois níveis de ruído (3% e 5%) são adicionados ao sinal de respostas para que esses ensaios se assemelhem aos ensaios experimentais, onde o ruído é inerente do processo. Já nos ensaios experimentais, apenas testes de vibração livre são executados. Diversos cenários de dano são propostos para as estruturas analisadas a fim de se verificar a robustez da rotina de detecção de dano. Os resultados mostram que a etapa de identificação modal estocástica através do método de identificação estocástica de subespaço (SSI) teve ótimos resultados, possibilitando, assim, a localização da região danificada da estrutura em todos os casos analisados.
Damage detection in large dimensions engineering structures through the analysis of their dynamic characteristics involves several fields. The first one deals with the structure modal identification parameter, since running free vibration tests in such structures is not a simple task, robust methods are needed in order to identify the modal parameters of this structure under ambient vibrations, this field is known as operational modal analysis. This work deals with the problem of damage detection in structures under ambient vibrations that can be represented by FEM using frame and beam elements. The damage location is determined through an optimization algorithm know as Backtracking Search Algorithm (BSA). It uses as objective function the identified natural frequencies and modes of vibration of the structure. Numerical and experimental tests are performed to assess the agreement of the methodology for both cases. For the numerical tests, more general cases of dynamic loads are used, and two noise levels (3% and 5%) are added to the response signal to assessing the robustness of the methodology close to the field conditions, in which noise is inherent of the process. In the experimental tests, only free vibration tests are performed. Several damage scenarios are proposed for the analyzed structures to check the robustness of the damage detection routine. The results show that the stochastic modal identification using the stochastic subspace identification (SSI) method had excellent results, thus allowing the location of the damaged region of the structure in all analyzed cases.

"Maintaining an efficient and reliable infrastructure requires continuous monitoring and control. In order to accomplish these tasks, algorithms are needed to process large sets of data and for modeling based on these processed data sets. For this reason, computationally efficient and accurate modeling algorithms along with data compression techniques and optimal yet practical control methods are in demand. These tools can help model structures and improve their performance. In this thesis, these two aspects are addressed separately. A principal component analysis based adaptive neuro-fuzzy inference system is proposed for fast and accurate modeling of time-dependent behavior of a structure integrated with a smart damper. Since a smart damper can only dissipate energy from structures, a challenge is to evaluate the dissipativity of optimal control methods for smart dampers to decide if the optimal controller can be realized using the smart damper. Therefore, a generalized deterministic definition for dissipativity is proposed and a commonly used controller, LQR is proved to be dissipative. Examples are provided to illustrate the effectiveness of the proposed modeling algorithm and evaluating the dissipativity of LQR control method. These examples illustrate the effectiveness of the proposed modeling algorithm and dissipativity of LQR controller."

This thesis considers the problem of performance modeling, analysis and control of capacitated re-entrant lines. Specifically, the first part of the thesis develops an analytical framework for the modeling, analysis and control of capacitated re-entrant lines, which is based on Generalized Stochastic Petri nets (GSPN) framework. The corresponding scheduling problem is systematically formulated, and the structure of the optimal policy is characterized and compared to that identified for "traditional" re-entrant lines. The second part of thesis addresses the problem of developing a systematic and computationally effective method for computing the optimal scheduling policy for any given configuration of capacitated re-entrant line. Specifically, the underlying scheduling problem is transformed to a Markov Decision Process (MDP) problem and an algorithm that systematically generates the MDP formulation for any given fab configuration is developed. The third part of thesis develops an effective approximating scheme based on the Neuro-Dynamic Programming (NDP) theory. In its general definition, the NDP method seeks the approximation of the optimal relative value function of the underlying MDP formulation by a parameterized function. Hence, an approximating structure for the considered problem is proposed and the quality of the generated approximations is systematically assessed. More specifically, this part of the thesis develops a set of "feature" functions and the mathematical apparatus necessary to evaluate the considered approximating scheme through a numerical experiment. The obtained results indicate that good quality approximations can be achieved by considering a set of features that characterize the distribution of the running process instances to the various processing stages and their lower order interactions. The last part of the thesis exploits the performance models developed in its earlier parts in order to provide an analytical characterization of the optimality of various deadlock resolution strategies for Markovian resource allocation systems under the objective of maximizing throughput.

Sequence alignment is one of the most intensely studied problems in bioinformatics, and is an important step in a wide range of analyses. An issue that has gained much attention in recent years is the fact that downstream analyses are often highly sensitive to the specific choice of alignment. One way to address this is to jointly sample alignments along with other parameters of interest. In order to extend the range of applicability of this approach, the first chapter of this thesis introduces a probabilistic evolutionary model for protein structures on a phylogenetic tree; since protein structures typically diverge much more slowly than sequences, this allows for more reliable detection of remote homologies, improving the accuracy of the resulting alignments and trees, and reducing sensitivity of the results to the choice of dataset. In order to carry out inference under such a model, a number of new Markov chain Monte Carlo approaches are developed, allowing for more efficient convergence and mixing on the high-dimensional parameter space. The second part of the thesis presents a directed acyclic graph (DAG)-based approach for representing a collection of sampled alignments. This DAG representation allows the initial collection of samples to be used to generate a larger set of alignments under the same approximate distribution, enabling posterior alignment probabilities to be estimated reliably from a reasonable number of samples. If desired, summary alignments can then be generated as maximum-weight paths through the DAG, under various types of loss or scoring functions. The acyclic nature of the graph also permits various other types of algorithms to be easily adapted to operate on the entire set of alignments in the DAG. In the final part of this work, methodology is introduced for alignment-DAG-based sequence annotation using hidden Markov models, and RNA secondary structure prediction using stochastic context-free grammars. Results on test datasets indicate that the additional information contained within the DAG allows for improved predictions, resulting in substantial gains over simply analysing a set of alignments one by one.

Helicopter rotor system operates in a highly dynamic and unsteady aerodynamic environment leading to severe vibratory loads on the rotor system. Repeated exposure to these severe loading conditions can induce damage in the composite rotor blade which may lead to a catastrophic failure. Therefore, an interest in the structural health monitoring (SHM) of the composite rotor blades has grown markedly in recent years. Two important issues are addressed in this thesis; (1) structural modeling and aeroelastic analysis of the damaged rotor blade and (2) development of a model based rotor health monitoring system. The effect of matrix cracking, the first failure mode in composites, is studied in detail for a circular section beam, box-beam and two-cell airfoil section beam. Later, the effects of further progressive damages such as debonding/delamination and fiber breakage are considered for a two-cell airfoil section beam representing a stiff-inplane helicopter rotor blade. It is found that the stiffness decreases rapidly in the initial phase of matrix cracking but becomes almost constant later as matrix crack saturation is reached. Due to matrix cracking, the bending and torsion stiffness losses at the point of matrix crack saturation are about 6-12 percent and about 25-30 percent, respectively. Due to debonding/delamination, the bending and torsion stiffness losses are about 6-8 percent and about 40-45 percent after matrix crack saturation, respectively. The stiffness loss due to fiber breakage is very rapid and leads to the final failure of the blade. An aeroelastic analysis is performed for the damaged composite rotor in forward flight and the numerically simulated results are used to develop an online health monitoring system. For fault detection, the variations in rotating frequencies, tip bending and torsion response, blade root loads and strains along the blade due to damage are investigated. It is found that peak-to-peak values of blade response and loads provide a good global damage indicator and result in considerable data reduction. Also, the shear strain is a useful indicator to predict local damage. The structural health monitoring system is developed using the physics based models to detect and locate damage from simulated noisy rotor system data. A genetic fuzzy system (GFS) developed for solving the inverse problem of detecting damage from noise contaminated measurements by hybridizing the best features of fuzzy logic and genetic algorithms. Using the changes in structural measurements between the damaged and undamaged blade, a fuzzy system is generated and the rule-base and membership functions optimized by genetic algorithm. The GFS is demonstrated using frequency and mode shape based measurements for various beam type structures such as uniform cantilever beam, tapered beam and non-rotating helicopter blade. The GFS is further demonstrated for predicting the internal state of the composite structures using an example of a composite hollow circular beam with matrix cracking damage mode. Finally, the GFS is applied for online SHM of a rotor in forward flight. It is found that the GFS shows excellent robustness with noisy data, missing measurements and degrades gradually in the presence of faulty sensors/measurements. Furthermore, the GFS can be developed in an automated manner resulting in an optimal solution to the inverse problem of SHM. Finally, the stiffness degradation of the composite rotor blade is correlated to the life consumption of the rotor blade and issues related to damage prognosis are addressed.

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We investigate strategies to define prediction models for a quality parameter of an industrial process. We estimate this variable using computational intelligence and in special regression methods. The main contribution of this paper is the comparative analysis of heuristic training models to create the prediction system. We propose two main paradigms to obtain the system, machine learning and hybrid artificial neural networks. The resulting system is a prototype for the intelligent supervision of a real-time production process. Statistical tools are used to compare the performance of the regression based predictor and the neuro-fuzzy based predictor, considering the degree of adaptation of the system to the problem and its generalization ability
Neste trabalho são investigadas estratégias para a elaboração de Modelos de Predição que possam ser utilizados no monitoramento de uma variável de qualidade pertencente a um determinado Processo Produtivo Industrial. Neste cenário, a variável de qualidade é estimada por meio de técnicas da Inteligência Computacional e empiricamente avaliada na resolução de problemas de regressão. A principal contribuição desta monografia é a análise comparativa de Técnicas da Inteligência Computacional associadas às estratégias heurísticas de treinamento para a construção dos Modelos de Predição. São propostas duas linhas de pesquisa investigadas a partir de uma pesquisa empírica dos dados, e analisados a partir de dois grandes ramos da Inteligência Computacional Aprendizagem de Máquina e Redes Neurais Híbridas. Os Modelos de Predição desenvolvidos são protótipos conceituais para potencial implementação de Sistemas Inteligentes em tempo real de uma planta industrial. O método de construção dos Modelos de Predição por técnicas de Regressão é comparado com o método de construção do Modelo de Predição por redes Neuro-Fuzzy e analisados por critérios estabelecidos a partir de ferramentas estatísticas que levam em consideração os níveis de adequação e generalização dos mesmos. Ao final, são apresentados resultados dos métodos implementados sobre a mesma base de dados bem como os pertinentes trabalhos futuros

This thesis describes a structural health monitoring (SHM) strategy to detect and classify changes in structures that can be equipped with sensors. SHM is an area of great interest, because its main objective is to verify the health of the structure to ensure its correct operation and, in turn, save maintenance costs. This objective is achieved by using algorithms and equipping the structure with a network of sensors that continuously monitor it. Researchers from around the world focus their efforts on the development of new forms of continuous monitoring to know the current state of the structure and to avoid possible failures or catastrophes. In this sense, in this work, a network of piezoelectric sensors (PZTs) is used for the development of the strategy of detection and classification of structural changes. This network of PZTs, attached to the surface of the structure to be diagnosed, applies vibrational excitation signals and, at the same time, collects the responses propagated through the structure. With this collected information, certain mathematical algorithms are developed. To carry out the main task of the proposed methodology, detection and classification of structural changes, the technique called t-distributed stochastic neighbor embedding (t-SNE) is essentially used. This technique is capable of representing the local structure of the high-dimensional data collected by the sensor network in two-dimensional or three-dimensional space. Furthermore, for the classification of structural changes, the detection methodology is expanded by adding the use of three strategies: (a) the smallest point-centroid distance; (b) the majority vote; and (c) the sum of the inverses of the distances. The methodology proposed in this study is tested and validated using an aluminum plate equipped with four PZT sensors and for certain predefined structural changes. The promising results obtained show the great classification capacity and the strong performance of this methodology, successfully classifying about 100% of the cases in various experimental scenarios. The main contribution of this project is the combination of the t-SNE technique with a carefully selected pre-processing of the data and with the three proposed classification strategies. This combination significantly improves the quality of the groups or clusters obtained with the damage detection and classification method, which represent the different structural states. Likewise, said combination diagnoses a structure with a low computational cost and high reliability. Regarding the applicability of the suggested strategy, there is no prescribed field of application: if a network of sensors can be installed in the structure to be diagnosed and several phases of action can be considered, the approach presented here can be, a priori, implemented.
Esta tesis describe una estrategia de monitorización de la salud estructural (SHM, por sus siglas en inglés) para detectar y clasificar fallos en estructuras que pueden ser equipadas con sensores. La SHM es un área de gran interés, ya que su objetivo principal es la verificación de la salud de la estructura para asegurar su correcto funcionamiento y, a su vez, ahorrar costes de mantenimiento. Este objetivo se consigue haciendo uso de algoritmos y equipando a la estructura con una red de sensores que la monitorizan de forma continuada. Investigadores de todo el mundo centran sus esfuerzos en el desarrollo de nuevas formas de monitorización continua para conocer el estado actual de la estructura y evitar posibles fallos o catástrofes. En este sentido, en este trabajo, se utiliza una red de sensores piezoeléctricos (PZT, por sus siglas en inglés) para el desarrollo de la estrategia de detección y clasificación de los cambios estructurales. Esta red de PZT, adherida a la superficie de la estructura a diagnosticar, aplica señales vibracionales de excitación y al mismo tiempo recoge las respuestas propagadas a través de la estructura. Con esta información recopilada se desarrollan ciertos algoritmos matemáticos. Para llevar a cabo la tarea principal de la metodología propuesta, detección y clasificación de fallos, se utiliza esencialmente la técnica denominada t-distributed stochastic neighbor embedding (t-SNE). Dicha técnica es capaz de representar la estructura local de los datos de alta dimensionalidad recopilados por la red de sensores en un espacio bidimensional o tridimensional. Además, para la clasificación de los cambios estructurales, se amplía la metodología de detección añadiendo el uso de tres estrategias: (a) la distancia punto-centroide más pequeña; (b) el voto mayoritario; y (c) la suma de las inversas de las distancias. La metodología propuesta en este estudio se prueba y valida utilizando una placa de aluminio equipada con cuatro sensores PZT y para ciertos daños predefinidos. Los prometedores resultados obtenidos ponen de manifiesto la gran capacidad de clasificación y el fuerte rendimiento de esta metodología, clasificando con éxito cerca del 100% de los casos en varios escenarios experimentales. La principal contribución de este proyecto es la combinación de la técnica t-SNE con un preprocesamiento de los datos cuidosamente seleccionado y con las tres estrategias de clasificación propuestas. Esta combinación mejora significativamente la calidad de los grupos o clústeres obtenidos con el método de detección y clasificación de daños, que representan los diferentes estados estructurales. Asimismo, dicha combinación diagnostica una estructura con un bajo coste computacional y una alta fiabilidad. En cuanto a la aplicabilidad de la estrategia sugerida, no hay un campo de aplicación prescrito: si se puede instalar una red de sensores en la estructura a diagnosticar y se pueden considerar varias fases de actuación, el enfoque aquí presentado puede implementarse a priori.

This thesis uses innovative approaches to analyse energy policy interventions aimed at enhancing the environmental sustainability of energy use as well as its consequential welfare implications. First, we examine the relationship between energy efficiency improvement and CO2 emissions at the macro level. We use the Index Decomposition Analysis to derive energy efficiency by separating out the impact of shifts in economic activity on energy intensity. We then employ econometric models to relate energy efficiency and CO2 emissions accounting for non-economic factors such as consumers lifestyle and attitudes. The applications for 13 OPEC and 30 OECD countries show that at the country-group and individual country level, increase in energy intensity for OPEC is associated with both deteriorations in energy efficiency and shifts towards energy-intensive activities. The model results suggest that the reduction in energy efficiency in general go in tandem with substantial increases in CO2 emissions. The decline in energy intensity for OECD can be attributed mainly to improvements in energy efficiency which is found to compensate for the impact on CO2 emissions of income changes. The results confirm the empirical relevance of energy efficiency improvements for the mitigation of CO2 emissions. The method developed in this chapter further enables the separate assessment of non-economic behavioural factors which according to the results exert a non-trivial influence on CO2 emissions. Secondly, having empirically confirmed the relationship between energy efficiency improvements and CO2 emission at the macro level in Chapter 2, we investigate potential underlying drivers of energy efficiency improvements taking into account potential asymmetric effects of energy price change in Chapter 3. This is crucial for designing effective and efficient policy measures that can promote energy efficiency. In addition to the Index Decomposition Analysis used to estimate the economy-wide energy efficiency in Chapter 2, we also use Stochastic Frontier Analysis and Data Envelop Analysis as alternative methods. The driving factors are examined using static and dynamic panel model methods that account for both observed and unobserved country heterogeneity. The application for 32 OECD countries shows that none of the three methods leads to correspondence in term of ranking between energy efficiency estimates and energy intensity at the country level corroborating the criticism that energy intensity is a poor proxy for energy efficiency. The panel-data regression results using the results of the three methods show similarities in the impacts of the determinants on the energy efficiency levels. Also, we find insignificant evidence of asymmetric effects of total energy price but there is proof of asymmetry using energy specific prices. Thirdly, in Chapter 4 we offer an improved understanding of the impacts to expect of abolishing fuel price subsidy on fuel consumption, and also of the welfare and distributional impacts at the household level. We develop a two-step approach for this purpose. Key aspect of the first step is a two-stage budgeting model to estimate various fuel types elasticities using micro-data. Relying on these estimates and the information on households expenditure shares for different commodities, the second step estimates the welfare (direct and indirect) and distributional impacts. The application for Nigeria emphasises the relevance of this approach. We find heterogeneous elasticities of fuel demand among household groups. The distributional impact of abolishing the kerosene subsidy shows a regressive welfare loss. Although we find a progressive loss for petrol, the loss gap between the low- and high-income groups is small relative to the loss gap from stopping kerosene subsidy, making the low-income groups to suffer a higher total welfare loss. Finally, from the highlighted results, we draw the following concluding remarks in chapter 5. Energy efficiency appears a key option to mitigate CO2 emissions but there is also a need for additional policies aiming for behavioural change; energy specific prices and allowing for asymmetry in analysing the changes in energy efficiency is more appropriate and informative in formulating reliable energy policies; the hypothesis that only the rich would be worse-off from fuel subsidy removal is rejected and the results further suggest that timing of the fuel subsidy removal would be crucial as a higher international oil price will lead to higher deregulated fuel price and consequently, larger welfare loss.

Les structures de génie civil, en particulier les ponts en béton armé, doivent être conçues et gérées pour assurer les besoins de transport et de communication dans la société. Il est indispensable de garantir un fonctionnement convenable et sécuritaire de ces structures, puisque les défaillances peuvent conduire à des perturbations du transport, des pertes catastrophiques de concessions et des pertes de vies humaines, avec des impacts économiques, sociétaux et environnementaux graves, à court et à long termes. Les gestionnaires entreprennent diverses activités pour maintenir la performance et le fonctionnement adéquat à long terme, tout en satisfaisant les contraintes financières et sécuritaires. Idéalement, ils peuvent recourir à des techniques d'optimisation pour établir les compromis entre la réduction du coût du cycle de vie (LCC) et la maximisation de la durée de vie. Cela nécessite le développement de l’analyse du cycle de vie, de l’analyse de fiabilité et de l'optimisation structurale.Les approches actuelles pour la conception et la gestion des structures s’appuyant sur l’analyse du coût de cycle de vie, montrent les besoins suivants : (1) une approche intégrée et systématique pour modéliser de façon cohérente les processus de dégradation, les charges de trafic, le vieillissement et les conséquences directes et indirectes de la défaillance, (2) une considération complète des dépendances économiques, structurales et stochastiques entre les différents éléments de l’ouvrage, (3) une approche permettant de modéliser efficacement un système structural formé de plusieurs éléments interdépendants, (4) une évaluation des conséquences de la dégradation et de la redistribution des charges entre les éléments en tenant compte de la redondance du système et de la configuration de l’ouvrage, (5) une méthode d'optimisation de la conception et de la maintenance qui préserve l’exigence de fiabilité tout en considérant la robustesse de la décision. L'objectif global de cette thèse est de fournir des procédures améliorées qui peuvent être appliquées à la conception et à la gestion fiabilistes et robustes des ouvrages en béton armé, en réduisant les coûts supportés par les gestionnaires et les utilisateurs, tout en tenant compte des dépendances entre les éléments. Dans la première partie de cette thèse, une synthèse bibliographique concernant les procédures de la conception et de la maintenance basée sur des calculs fiabilistes est présentée, et les différents composants du LCC sont développés. Ensuite, une approche est proposée pour la conception des ouvrages en tenant compte du coût aux usagers et en intégrant dans la fonction du coût de cycle de vie. Le modèle couplé corrosion-fatigue est aussi considéré dans l’optimisation de la conception. La planification de la maintenance des ouvrages est ensuite développée, en considérant les différents types d'interaction entre les éléments, en particulier les dépendances économiques, structurales et stochastiques. Ce modèle utilise l'analyse de l'arbre de défaillance et les probabilités conditionnelles pour tenir compte des dépendances dans la planification de la maintenance. Les conséquences de la dégradation et de la redistribution des charges sont prises en compte dans l'approche proposée. Par ailleurs, une méthode pratique de calcul de la fiabilité d'un système formé de plusieurs composantes interdépendantes est proposée, à travers un facteur de redondance calculé par la modélisation mécanique. Enfin, une nouvelle procédure d'optimisation est proposée, permettant de tenir compte des incertitudes dans le système et la capacité structurale de s'adapter aux variabilités intrinsèques. La procédure proposée tient compte des incertitudes et de la variabilité dans une formulation cohérente, validée au moyen des applications numériques. (...)
Civil engineering structures, particularly reinforced concrete bridges, should be designed and managed to ensure the society needs. It is crucial to assure that these structures function properly and safely as damage during the service life can lead to transport disturbance, catastrophic loss of property, causalities, as well as severe economic, social, and environmental impacts, in addition to long term consequences. Decision-makers adopt various activities to maintain adequate long-term performance and functionality while satisfying financial constraints. Ideally, they may employ optimization techniques to identify the trade-offs between minimizing the life-cycle cost (LCC) and maximizing the expected service life. This requires the development of three challenging chores: life cycle analysis, reliability analysis and structural optimization. The current approaches for the design and management of structures through a Life-cycle cost analysis (LCCA) highlight the following needs: (1) an integrated and systematic approach to model coherently the deterioration processes, the increasing traffic loads, the aging and the direct and indirect consequences of failure, (2) a mutual consideration of economic, structural and stochastic dependencies between the elements of a structural system, (3) an adequate approach for the deterioration dependencies and load redistribution between the elements, (4) an improvement of system reliability computation as a function of the structural redundancy and configuration that can take into account the dependencies between the elements, (5) a consideration of design and maintenance optimization procedures that focus coherently on the robustness of the management decision and on the satisfaction of reliability requirements.The overall objective of this study is to provide improved LCCA and procedures that can be applied to select optimal and robust design and maintenance decisions regarding new and existing reinforced concrete structures, by minimizing both manager and user costs, while providing the required safety along the structure lifetime, taking into account the most severe degradation processes and the dependencies between structural elements. In the first part of this thesis, a literature review concerning the current probabilistic design and maintenance procedures is presented, and the LCC components are discussed. Then, a new approach is developed to evaluate the user delay costs on a reinforced concrete bridge structure, based on direct and indirect costs related to degradation and failure, and to integrate it to the life cycle cost function, in order to allow for probabilistic design. In addition,the coupled corrosion-fatigue model is considered in the design optimization. Afterward, a structural maintenance planning approach is developed to consider the three types of interactions, namely economic, structural and stochastic dependencies. The proposed model uses fault tree analysis and conditional probabilities to reflect the dependencies in the maintenance planning. The consequences of degradation are evaluated and a method is proposed to account for the load redistribution. Moreover, a practical formulation for quantifying the reliability of a system formed of interrelated components is proposed, by the mean of a redundancy factor that can be computed by finite element analysis. Finally, a new optimization procedure is proposed, by taking into account the uncertainties in the analysis, and the structural ability to adapt to variability, unforeseen actions or deterioration mechanisms. The proposed procedure takes account of uncertainties andvariability in one consistent formulation, which is shown through numerical applications. (...)

Conselho Nacional de Desenvolvimento Científico e Tecnológico
The basic concept of impedance-based structure health monitoring is measuring the variation of the electromechanical impedance of the structure as caused by the presence of damage by using patches of piezoelectric material bonded on the surface of the structure (or embedded into). The measured electrical impedance of the PZT patch is directly related to the mechanical impedance of the structure. That is why the presence of damage can be detected by monitoring the variation of the impedance signal. In order to quantify damage, a metric is specially defined, which allows to assign a characteristic scalar value to the fault. This study initially evaluates the influence of environmental conditions in the impedance measurement, such as temperature, magnetic fields and ionic environment. The results show that the magnetic field does not influence the impedance measurement and that the ionic environment influences the results. However, when the sensor is shielded, the effect of the ionic environment is significantly reduced. The influence of the sensor geometry has also been studied. It has been established that the shape of the PZT patch (rectangular or circular) has no influence on the impedance measurement. However, the position of the sensor is an important issue to correctly detect damage. This work presents the development of a low-cost portable system for impedance measuring to automatically measure and store data from 16 PZT patches, without human intervention. One fundamental aspect in the context of this work is to characterize the damage type from the various impedance signals collected. In this sense, the techniques of artificial intelligence known as neural networks and fuzzy cluster analysis were tested for classifying damage of aircraft structures, obtaining satisfactory results. One last contribution of the present work is the study of the performance of the electromechanical impedance-based structural health monitoring technique to detect damage in structures under dynamic loading. Encouraging results were obtained for this aim.
O conceito básico da técnica de integridade estrutural baseada na impedância tem a ver com o monitoramento da variação da impedância eletromecânica da estrutura, causada pela presença alterações estruturais, através de pastilhas de material piezelétrico coladas na superfície da estrutura ou nela incorporadas. A impedância medida se relaciona com a impedância mecânica da estrutura. A partir da variação dos sinais de impedância pode-se concluir pela existência ou não de uma falha. Para quantificar esta falha, métricas de dano são especialmente definidas, permitindo atribuir-lhe um valor escalar característico. Este trabalho pretende inicialmente avaliar a influência de algumas condições ambientais, tais como os campos magnéticos e os meios iônicos na medição de impedância. Os resultados obtidos mostram que os campos magnéticos não tem influência na medição de impedância e que os meios iônicos influenciam os resultados; entretanto, ao blindar o sensor, este efeito se reduz consideravelmente. Também foi estudada a influencia da geometria, ou seja, do formato do PZT e da posição do sensor com respeito ao dano. Verificou-se que o formato do PZT não tem nenhuma influência na medição e que a posição do sensor é importante para detectar corretamente o dano. Neste trabalho se apresenta o desenvolvimento de um sistema de medição de impedância de baixo custo e portátil que tem a capacidade de medir e armazenar a medição de 16 PZTs sem a necessidade de intervenção humana. Um aspecto de fundamental importância no contexto deste trabalho é a caracterização do dano a partir dos sinais de impedância coletados. Neste sentido, as técnicas de inteligência artificial conhecidas como redes neurais e análises de cluster fuzzy, foram testadas para classificar danos em estruturas aeronáuticas, obtendo resultados satisfatórios para esta tarefa. Uma última contribuição deste trabalho é o estudo do comportamento da técnica de monitoramento de integridade estrutural baseado na impedância eletromecânica na detecção de danos em estruturas submetidas a carregamento dinâmico. Os resultados obtidos mostram que a técnica funciona adequadamente nestes casos.
Doutor em Engenharia Mecânica

The objective of this thesis is to develop a novel methodology of fractional stochastic dynamics to study stochastic stability of viscoelastic systems under stochastic loadings. Numerous structures in civil engineering are driven by dynamic forces, such as seismic and wind loads, which can be described satisfactorily only by using probabilistic models, such as white noise processes, real noise processes, or bounded noise processes. Viscoelastic materials exhibit time-dependent stress relaxation and creep; it has been shown that fractional calculus provide a unique and powerful mathematical tool to model such a hereditary property. Investigation of stochastic stability of viscoelastic systems with fractional calculus frequently leads to a parametrized family of fractional stochastic differential equations of motion. Parametric excitation may cause parametric resonance or instability, which is more dangerous than ordinary resonance as it is characterized by exponential growth of the response amplitudes even in the presence of damping. The Lyapunov exponents and moment Lyapunov exponents provide not only the information about stability or instability of stochastic systems, but also how rapidly the response grows or diminishes with time. Lyapunov exponents characterizes sample stability or instability. However, this sample stability cannot assure the moment stability. Hence, to obtain a complete picture of the dynamic stability, it is important to study both the top Lyapunov exponent and the moment Lyapunov exponent. Unfortunately, it is very difficult to obtain the accurate values of theses two exponents. One has to resort to numerical and approximate approaches. The main contributions of this thesis are: (1) A new numerical simulation method is proposed to determine moment Lyapunov exponents of fractional stochastic systems, in which three steps are involved: discretization of fractional derivatives, numerical solution of the fractional equation, and an algorithm for calculating Lyapunov exponents from small data sets. (2) Higher-order stochastic averaging method is developed and applied to investigate stochastic stability of fractional viscoelastic single-degree-of-freedom structures under white noise, real noise, or bounded noise excitation. (3) For two-degree-of-freedom coupled non-gyroscopic and gyroscopic viscoelastic systems under random excitation, the Stratonovich equations of motion are set up, and then decoupled into four-dimensional Ito stochastic differential equations, by making use of the method of stochastic averaging for the non-viscoelastic terms and the method of Larionov for viscoelastic terms. An elegant scheme for formulating the eigenvalue problems is presented by using Khasminskii and Wedig’s mathematical transformations from the decoupled Ito equations. Moment Lyapunov exponents are approximately determined by solving the eigenvalue problems through Fourier series expansion. Stability boundaries, critical excitations, and stability index are obtained. The effects of various parameters on the stochastic stability of the system are discussed. Parametric resonances are studied in detail. Approximate analytical results are confirmed by numerical simulations.

Stochastic analysis procedures have been recently applied to analyze nonlinear dynamical systems. In this study, nonlinear responses, stochastic and/or chaotic, are examined and interpreted from a probabilistic perspective. A multi-point-moored ocean structural system under regular and irregular wave excitations is analytically examined via a generalized stochastic Melnikov function and Markov process approach. Time domain simulations and associated experimental observations are employed to assist in the interpretation of the analytical predictions. Taking into account the presence of random noise, a generalized stochastic Melnikov function associated with the corresponding averaged system, where a homoclinic connection exists near the primary resonance, is derived. The effects of random noise on the boundary of regions of possible existence of chaotic response is demonstrated via a mean-squared Melnikov criterion. The random wave field is approximated as random perturbations on regular and nearly regular (with very narrow-band spectrum) waves by adding a white noise component, or using a filtered white noise process to fit the JONSWAP spectrum. A Markov process approach is then applied explicitly to analyze the response. The evolution of the probability density function (PDF) of nonlinear stochastic response under the Markov process approach is characterized by a deterministic partial differential equation called the Fokker-Planck equation, which in this study is solved by a path integral solution procedure. Numerical evaluation of the path integral solution is based on path sum, and the short-time propagator is discretized accordingly. Short-time propagation is performed by using a fourth order Runge-Kutta scheme to calculate the most probable (i.e. mean) position in the phase space and to establish the fact that discrete contributions to the random response are locally Gaussian. Transient and steady-state PDF's can be obtained by repeat application of the short-time propagation. Based on depictions of the joint probability density functions and time domain simulations, it is observed that the presence of random noise may expedite the occurrence of "noisy" chaotic response. The noise intensity governs the transition among various types of stochastic nonlinear responses and the relative strengths of coexisting response attractors. Experimental observations confirm the general behavior depicted by the analytical predictions.
Graduation date: 1995

Wai-tung Ho.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1992.
Includes bibliographical references (leaves 81-83).
Chapter CHAPTER 1 --- OVERVIEW OF CONSTRAINTED ESTIMATION OF STRUCTURAL EQUATION MODEL --- p.1
Chapter CHAPTER 2 --- MULTISAMPLE ANALYSIS OF STRUCTURAL EQUATION MODELS WITH STOCHASTIC CONSTRAINTS --- p.4
Chapter 2.1 --- The Basic Model --- p.4
Chapter 2.2 --- Bayesian Approach to Nuisance Parameters --- p.5
Chapter 2.3 --- Estimation and Algorithm --- p.8
Chapter 2.4 --- Asymptotic Properties of the Bayesian Estimate --- p.11
Chapter CHAPTER 3 --- MULTISAMPLE ANALYSIS OF STRUCTURAL EQUATION MODELS WITH EXACT AND STOCHASTIC CONSTRAINTS --- p.17
Chapter 3.1 --- The Basic Model --- p.17
Chapter 3.2 --- Bayesian Approach to Nuisance Parameters and Estimation Procedures --- p.18
Chapter 3.3 --- Asymptotic Properties of the Bayesian Estimate --- p.20
Chapter CHAPTER 4 --- SIMULATION STUDIES AND NUMERICAL EXAMPLE --- p.24
Chapter 4.1 --- Simulation Study for Identified Models with Stochastic Constraints --- p.24
Chapter 4.2 --- Simulation Study for Non-identified Models with Stochastic Constraints --- p.29
Chapter 4.3 --- Numerical Example with Exact and Stochastic Constraints --- p.32
Chapter CHAPTER 5 --- DISCUSSION AND CONCLUSION --- p.34
APPENDICES --- p.36
TABLES --- p.66
REFERENCES --- p.81

Choy Man Wah Minnie.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 83).
Abstracts in English and Chinese.
Abstract --- p.i
Acknowledgement --- p.iii
Chapter 1 --- Introduction --- p.1
Chapter 2 --- The Analysis of APT using SEM --- p.3
Chapter 2.1 --- The APT model --- p.3
Chapter 2.2 --- The structural equation model approach --- p.5
Chapter 3 --- Incorporating stochastic constraints into the SEM analysis of APT --- p.8
Chapter 3.1 --- Introduction --- p.8
Chapter 3.2 --- Bayesian analysis of stochastic constraints --- p.9
Chapter 3.3 --- Three types of structures for T I --- p.10
Chapter 3.3.1 --- Case 1: T = (σ2Imxm --- p.10
Chapter 3.3.2 --- "Case 2: r is a diagonal matrix with diagonal elements σ2j for = 1， …,m" --- p.13
Chapter 3.3.3 --- Case 3: Γ is a general positive definite matrix --- p.14
Chapter 3.4 --- Estimation of parameters using the Mx program --- p.16
Chapter 4 --- Empirical study on Hong Kong stock market --- p.17
Chapter 4.1 --- Information of data --- p.17
Chapter 4.2 --- Source of data --- p.17
Chapter 4.3 --- Lisrel model with exact constraints --- p.19
Chapter 4.3.1 --- The resultant model --- p.20
Chapter 4.4 --- Lisrel model with stochastic constraints --- p.21
Chapter 4.4.1 --- Result --- p.22
Chapter 5 --- Simulation study --- p.35
Chapter 5.1 --- Simulation design --- p.35
Chapter 5.2 --- Simulation procedure --- p.40
Chapter 5.3 --- Simulation result --- p.41
Chapter 5.3.1 --- Sample size --- p.41
Chapter 5.3.2 --- Analysis methods (constraints) --- p.42
Chapter 5.3.3 --- Factor loadings --- p.43
Chapter 5.3.4 --- Factor correlation matrix --- p.43
Chapter 5.3.5 --- Risk premia --- p.43
Chapter 5.3.6 --- Overall result --- p.44
Chapter 6 --- Conclusion and discussion --- p.45
Appendices --- p.46
Chapter A --- Simulation result - Mean --- p.47
Chapter B --- Simulation result - Bias --- p.56
Chapter C --- Simulation result - RMSE --- p.65
Chapter D --- Mx input script --- p.74
Chapter D.l --- Stochastic constraints Case 1 --- p.74
Chapter D.2 --- Stochastic constraints Case 2 --- p.77
Chapter D.3 --- Stochastic constraints Case 3 --- p.80
Bibliography --- p.83

碩士
國立臺灣海洋大學
輪機工程系
97
In this thesis、we introduce the passive properties and discrete stochastic T-S fuzzy model for stability analysis and controller synthesis. The external disturbance input is considered such as power supply in passivity theory and it is also considered for the controller design procedure. Besides、the T-S fuzzy model can present the complex nonlinear dynamic system via several sub-linear systems with the membership function which related of each sub-linear system. The proposed fuzzy controller is developed based on Parallel Distribution Compensation (PDC) technique. Through the Lyapunov stability criterion、passivity theory and Linear Matrix Inequality (LMI) algorithm、the problems of stability analysis and controller design are discussed in this thesis. Finally、example of discrete fuzzy control system for ship steering is provided to show the application of the approaches of this thesis.

Analysis of vibration of systems with uncertainty in material properties under the influence of a random forcing function is an active area of research. Especially the characterization based on mode shapes and frequencies of linear vibrating systems leads to much discussed random eigenvalue problem, which repeatedly appears while analyzing a number of engineering systems. Such analyses with conventional schemes for significant variation of system parameters for large systems are often not viable because of the high computational costs involved. Appropriate tools to reduce the size of stochastic vibrating systems and efficient response calculation are yet to mature. Among the mathematical tools used in this case, polynomial chaos formulation of uncertainties shows promise. But this comes with the implementation issue of solving large systems of nonlinear equations arising from Bubnov-Galerking projection in the formulation. This dissertation reports the study of such dynamic systems with uncertainties characterized by the probability distribution of eigen solutions under a stochastic finite element framework. In the context of structural vibration, the determination of appropriate modes to be considered in a stochastic framework is not straightforward. In this dissertation, at first the choice of dominant modes in stochastic framework is studied for vibration problems. A relative measure, based on the average energy contribution of each mode to the system, is developed. Further the interdependence of modes and the effect of the shape of the load on the choice of dominant modes are studied. Using these considerations, a hybrid algorithm is developed based on polynomial chaos framework for the response analysis of a structure with random mass and sickness and under the influence of random force. This is done by using modal truncation for response analysis with in a Monte Carlo loop. The algorithm is observed to be more efficient and achieves a high degree of accuracy compared to conventional techniques. Considering the fact that the Monte Carlo loops within the above mentioned hybrid algorithm is easily parallelizable, the efficient implementation of it depends on the SFE solution. The set of nonlinear equations arising from polynomial chaos formulation is solved using matrix-free Newton’s iteration using GMRES as linear solver. Solution of a large system using a iterative method like GMRES necessitates the use of a good preconditioner. Keeping focus on the par-allelizability of the algorithm, a number of efficient but cheap-to-construct preconditioners are developed and the most effective among them is chosen. The solution process is parallelized for large systems. The scalability of solution process in conjunction with the preconditioner is studied in details.

In order to fight identity fraud, the use of a reliable personal identifier has become a necessity. Fingerprints are considered one of the best biometric measurements and are used as a universal personal identifier. There are two main phases in the recognition of personal identity using fingerprints: 1) extraction of suitable features of fingerprints, and 2) fingerprint matching making use of the extracted features to find the correspondence and similarity between the fingerprint images. Use of global features in minutia-based fingerprint recognition schemes enhances their recognition capability but at the expense of a substantially increased complexity. The recognition accuracies of most of the fingerprint recognition schemes, which rely on some sort of crisp clustering of the fingerprint features, are adversely affected due to the problems associated with the behavioral and anatomical characteristics of the fingerprints. The objective of this research is to develop efficient and cost-effective techniques for fingerprint recognition, that can meet the challenges arising from using both the local and global features of the fingerprints as well as effectively deal with the problems resulting from the crisp clustering of the fingerprint features. To this end, the structural information of local and global features of fingerprints are used for their decomposition, representation and matching in a multilevel hierarchical framework. The problems associated with the crisp clustering of the fingerprint features are addressed by incorporating the ideas of fuzzy logic in developing the various stages of the proposed fingerprint recognition scheme. In the first part of this thesis, a novel low-complexity multilevel structural scheme for fingerprint recognition (MSFR) is proposed by first decomposing fingerprint images into regions based on crisp partitioning of some global features of the fingerprints. Then, multilevel feature vectors representing the structural information of the fingerprints are formulated by employing both the global and local features, and a fast multilevel matching algorithm using this representation is devised. Inspired by the ability of fuzzy-based clustering techniques in dealing more effectively with the natural patterns, in the second part of the thesis, a new fuzzy based clustering technique that can deal with the partitioning problem of the fingerprint having the behavioral and anatomical characteristics is proposed and then used to develop a fuzzy based multilevel structural fingerprint recognition scheme. First, a histogram analysis fuzzy c-means (HA-FCM) clustering technique is devised for the partitioning of the fingerprints. The parameters of this partitioning technique, i.e., the number of clusters and the set of initial cluster centers, are determined in an automated manner by employing the histogram of the fingerprint orientation field. The development of the HA-FCM partitioning scheme is further pursued to devise an enhanced HA-FCM (EAH-FCM) algorithm. In this algorithm, the smoothness of the fingerprint partitioning is improved through a regularization of the fingerprint orientation field, and the computational complexity is reduced by decreasing the number of operations and by increasing the convergence rate of the underlying iterative process of the HA-FCM technique. Finally, a new fuzzy based fingerprint recognition scheme (FMSFR), based on the EHA-FCM partitioning scheme and the basic ideas used in the development of the MSFR scheme, is proposed. Extensive experiments are conducted throughout this thesis using a number of challenging benchmark databases. These databases are selected from the FVC2002, FVC2004 and FVC2006 competitions containing a wide variety of challenges for fingerprint recognition. Simulation results demonstrate not only the effectiveness of the proposed techniques and schemes but also their superiority over some of the state-of-the-art techniques, in terms of the recognition accuracy and the computational complexity.

Uncertainty propagation in engineering mechanics and dynamics is a highly challenging problem that requires development of analytical/numerical techniques for determining the stochastic response of complex engineering systems. In this regard, although Monte Carlo simulation (MCS) has been the most versatile technique for addressing the above problem, it can become computationally daunting when faced with high-dimensional systems or with computing very low probability events. Thus, there is a demand for pursuing more computationally efficient methodologies. Further, most structural systems are likely to exhibit nonlinear and time-varying behavior when subjected to extreme events such as severe earthquake, wind and sea wave excitations. In such cases, a reliable identification approach is behavior and for assessing its reliability. Current work addresses two research themes in the field of stochastic engineering dynamics related to the above challenges. In the first part of the dissertation, the recently developedWiener Path Integral (WPI) technique for determining the joint response probability density function (PDF) of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output of a filter equation with Gaussian white noise as its input, it is possible to define an augmented response vector process to be considered in the WPI solution technique. A significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms. In such cases, it is shown that the use of a filter approximation facilitates the implementation of the WPI technique in a straightforward manner, without compromising its accuracy necessarily. Further, in addition to dynamical systems subject to stochastic excitation, the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as non-Gaussian and non-homogeneous stochastic fields. Several numerical examples pertaining to both single- and multi-degree-of freedom systems are considered, including a marine structural system exposed to flow-induced non-white excitation, as well as a beam with a non-Gaussian and non-homogeneous Young’s modulus. Comparisons with MCS data demonstrate the accuracy of the technique. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear time-variant multi-degree-of-freedom oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear subsystems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sampling theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. A nonlinear time-variant system with fractional derivative elements is used as a numerical example to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

abstract: This dissertation applies the Bayesian approach as a method to improve the estimation efficiency of existing econometric tools. The first chapter suggests the Continuous Choice Bayesian (CCB) estimator which combines the Bayesian approach with the Continuous Choice (CC) estimator suggested by Imai and Keane (2004). Using simulation study, I provide two important findings. First, the CC estimator clearly has better finite sample properties compared to a frequently used Discrete Choice (DC) estimator. Second, the CCB estimator has better estimation efficiency when data size is relatively small and it still retains the advantage of the CC estimator over the DC estimator. The second chapter estimates baseball's managerial efficiency using a stochastic frontier function with the Bayesian approach. When I apply a stochastic frontier model to baseball panel data, the difficult part is that dataset often has a small number of periods, which result in large estimation variance. To overcome this problem, I apply the Bayesian approach to a stochastic frontier analysis. I compare the confidence interval of efficiencies from the Bayesian estimator with the classical frequentist confidence interval. Simulation results show that when I use the Bayesian approach, I achieve smaller estimation variance while I do not lose any reliability in a point estimation. Then, I apply the Bayesian stochastic frontier analysis to answer some interesting questions in baseball.
Dissertation/Thesis
Doctoral Dissertation Economics 2014

by Tung-lok Ng.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1990.
Bibliography: leaves 57-59.
Chapter Chapter 1 --- Introduction --- p.1
Chapter Chapter 2 --- Full Maximum Likelihood Estimation of the General Model --- p.4
Chapter 2.1 --- Introduction --- p.4
Chapter 2.2 --- Model --- p.4
Chapter 2.3 --- Identification of the model --- p.5
Chapter 2.4 --- Maximum likelihood estimation --- p.7
Chapter 2.5 --- Computational Procedure --- p.12
Chapter 2.6 --- Tests of Hypothesis --- p.13
Chapter 2.7 --- Example --- p.14
Chapter Chapter 3 --- Bayesian Analysis of Stochastic Prior Information --- p.17
Chapter 3.1 --- Introduction --- p.17
Chapter 3.2 --- Bayesian Analysis of the general model --- p.18
Chapter 3.3 --- Computational Procedure --- p.22
Chapter 3.4 --- Test the Compatibility of the Prior Information --- p.24
Chapter 3.5 --- Example --- p.25
Chapter Chapter 4 --- Simulation Study --- p.27
Chapter 4.1 --- Introduction --- p.27
Chapter 4.2 --- Simulation1 --- p.27
Chapter 4.3 --- Simulation2 --- p.30
Chapter 4.4 --- Summary and Discussion --- p.31
Chapter Chapter 5 --- Concluding Remarks --- p.33
Tables
References --- p.57

Conventional Cobb-Douglas and Transcendental Logarithmic production functions widely used in Stochastic Production Frontier Estimation and Inefficiency Analysis have merits and deficiencies. The Cobb-Douglas function imposes monotonicity and concavity constraints required by microeconomic theory. However it is inflexible and implies undesired assumptions as well. The Trans-log function is very flexible and does not imply undesired assumptions, yet it is very hard to impose both monotonicity and concavity constraints. The first essay introduced a class of stochastic production frontier estimation models that impose monotonicity and concavity constraints and suggested models that are very flexible. Researchers can use arbitrary order of polynomial functions or any function of independent variables within the suggested frameworks. Also shown was that adopting suggested models could greatly increase predictive accuracy through simulations. In the second essay we generalized the suggested models with the Inefficiency Analysis technique. In the last essay we extended the models developed in the previous two essays with regression spline and let the data decide how flexible or complicated the model should be. We showed the improvement of deterministic frontier estimation this extension could bring through simulations, as well. Works in this dissertation reduced the gap between conventional structural models and nonparametric models in stochastic frontier estimation field. This dissertation offered applied researchers Stochastic Production Frontier models that are more accurate and flexible than previous ones. It also preserves constraints of economic theory.

In many engineering applications, it is a formidable task to construct mathematical models that are expected to produce accurate predictions of the behavior of a system of interest. During the construction of such predictive models, errors due to imperfect modeling and uncertainties due to incomplete information about the system and its environment (e.g., input or excitation) always exist and can be accounted for appropriately by using probability logic. To assess the system performance subjected to dynamic excitations, a stochastic system analysis considering all the uncertainties involved has to be performed. In engineering, evaluating the robust failure probability (or its complement, robust reliability) of the system is a very important part of such stochastic system analysis. The word ‘robust’ is used because all uncertainties, including those due to modeling of the system, are taken into account during the system analysis, while the word ‘failure’ is used to refer to unacceptable behavior or unsatisfactory performance of the system output(s). Whenever possible, the system (or subsystem) output (or maybe input as well) should be measured to update models for the system so that a more robust evaluation of the system performance can be obtained. In this thesis, the focus is on stochastic system analysis, model and reliability updating of complex systems, with special attention to complex dynamic systems which can have high-dimensional uncertainties, which are known to be a very challenging problem. Here, full Bayesian model updating approach is adopted to provide a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying system and to its exclusive foundation on the probability axioms.

First, model updating of a complex system which can have high-dimensional uncertainties within a stochastic system model class is considered. To solve the challenging computational problems, stochastic simulation methods, which are reliable and robust to problem complexity, are proposed. The Hybrid Monte Carlo method is investigated and it is shown how this method can be used to solve Bayesian model updating problems of complex dynamic systems involving high-dimensional uncertainties. New formulae for Markov Chain convergence assessment are derived. Advanced hybrid Markov Chain Monte Carlo simulation algorithms are also presented in the end.

Next, the problem of how to select the most plausible model class from a set of competing candidate model classes for the system and how to obtain robust predictions from these model classes rigorously, based on data, is considered. To tackle this problem, Bayesian model class selection and averaging may be used, which is based on the posterior probability of different candidate classes for a system. However, these require calculation of the evidence of the model class based on the system data, which requires the computation of a multi-dimensional integral involving the product of the likelihood and prior defined by the model class. Methods for solving the computationally challenging problem of evidence calculation are reviewed and new methods using posterior samples are presented.

Multiple stochastic model classes can be created even there is only one embedded deterministic model. These model classes can be viewed as a generalization of the stochastic models considered in Kalman filtering to include uncertainties in the parameters characterizing the stochastic models. State-of-the-art algorithms are used to solve the challenging computational problems resulting from these extended model classes. Bayesian model class selection is used to evaluate the posterior probability of an extended model classe and the original one to allow a data-based comparison. The problem of calculating robust system reliability is also addressed. The importance and effectiveness of the proposed method is illustrated with examples for robust reliability updating of structural systems. Another significance of this work is to show the sensitivity of the results of stochastic analysis, especially the robust system reliability, to how the uncertainties are handled, which is often ignored in past studies.

A model validation problem is then considered where a series of experiments are conducted that involve collecting data from successively more complex subsystems and these data are to be used to predict the response of a related more complex system. A novel methodology based on Bayesian updating of hierarchical stochastic system model classes using such experimental data is proposed for uncertainty quantification and propagation, model validation, and robust prediction of the response of the target system. Recently-developed stochastic simulation methods are used to solve the computational problems involved.

Finally, a novel approach based on stochastic simulation methods is developed using current system data, to update the robust failure probability of a dynamic system which will be subjected to future uncertain dynamic excitations. Another problem of interest is to calculate the robust failure probability of a dynamic system during the time when the system is subjected to dynamic excitation, based on real-time measurements of some output from the system (with or without corresponding input data) and allowing for modeling uncertainties; this generalizes Kalman filtering to uncertain nonlinear dynamic systems. For this purpose, a novel approach is introduced based on stochastic simulation methods to update the reliability of a nonlinear dynamic system, potentially in real time if the calculations can be performed fast enough.

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 probabilistic methodology for the reliability analysis of composite rotor blades at the ply level was developed. The proposed methodology involves (i) the quantification of the uncertainties (physical, statistical and model) related to the material properties and the extreme aero-elastic loads based on experimental data as well as on 10 min load simulations respectively, (ii) the identification of the critical failure modes of the composite structure in terms of limit state functions and (iii) the selection of an appropriate reliability method to perform the analysis. It is pointed out that the reliability method should be able to handle the considerably large number of limit state function introduced by the ply level reliability approach and estimate the failure probability of the structure. To efficiently deal with the problem, an appropriate implementation of the Response Surface Method combined with crude Monte Carlo simulation was proposed. The methodology was implemented for two real rotor blade designs, namely a 30m Glass/Polyester and the 65m UPWIND reference rotor baled. Initially, calculations were performed for the first case study using a 3D shell FE formulation in a commercial probabilistic code. An efficient procedure was introduced to define the stochastic character of the concentrated loads acting on the 3D FE model starting from load time series of sectional stress resultants from aero-elastic beam simulations. For the first time such a detailed model was analyzed and assessed in a probabilistic base. Nevertheless, a considerable CPU time was in need for the performance of such a reliability analysis. The development of an efficient probabilistic tool capable to perform consecutive reliability analyses at the ply level of the composite rotor blade structure and prove valuable for the probabilistic design was carried out. To demonstrate the efficiency of the developed tool, the impact of various probabilistic modelling assumptions directly on the β-index value of a rotor blade design was studied.
Στην παρούσα διατριβή αναπτύχθηκε στοχαστική μεθοδολογία για την αποτίμηση αξιοπιστίας πτερυγίων ανεμογεννητριών από σύνθετα υλικά, στο επίπεδο της στρώσης, υπό ακραία στατική φόρτιση. Η προτεινόμενη μεθοδολογία περιλαμβάνει (i) την ποσοτικοποίηση αβεβαιοτήτων (φυσική, στατιστική και αβεβαιότητα μοντέλου) που σχετίζονται με τις βασικές παραμέτρους του πτερυγίου (υλικά και φορτία) στηριζόμενη σε ένα μεγάλο αριθμό πειραμάτων για τον προσδιορισμό των μηχανικών ιδιοτήτων του συνθέτου υλικού καθώς και 10-λεπτες αεροελαστικές χρονοσειρές για την ακραία στατική φόρτιση (ii) την αναγνώριση όλων των σημαντικών μηχανισμών αστοχίας της κατασκευής και την έκφρασή τους στη μορφή οριακών συναρτήσεων αστοχίας και (iii) την επιλογή μίας κατάλληλης μεθόδου αξιοπιστίας. Σημειώνεται ότι η μέθοδος αξιοπιστίας θα πρέπει να είναι ικανή να διαχειρίζεται ένα πολύ μεγάλο αριθμό οριακών συναρτήσεων αστοχίας όπως επιβάλει η ανάλυση αξιοπιστίας στο επίπεδο της στρώσης της κατασκευής. Για το σκοπό αυτό προτάθηκε μια κατάλληλη τροποποίηση της Response Surface Method τεχνικής η οποία συνδυάστηκε με την μέθοδο προσομοίωσης crude Monte Carlo. Η προτεινόμενη στοχαστική μεθοδολογία εφαρμόστηκε για την περίπτωση δυο πραγματικών πτερυγίων: ενός 30 m Glass/Polyester και του 65 m Glass/Epoxy (UPWIND) πτερυγίου. Η ανάλυση αρχικά πραγματοποιήθηκε σε γενικού σκοπού στοχαστικά εργαλεία κάνοντας χρήση τρισδιάστατου μοντέλου πεπερασμένων στοιχείων. Σημειώνεται ότι ο υπολογισμός των φορτίων από αεροελαστικούς κώδικες υλοποιείται πάντα στη βάση στοιχείων δοκού. Προτάθηκε επομένως διαδικασία για την στοχαστική αναπαράσταση των συγκεντρωμένων δυνάμεων που επιβάλλονται στο τρισδιάστατο μοντέλο πεπερασμένων στοιχείων του πτερυγίου στηριζόμενη σε χρονοσειρές εσωτερικών αντιδράσεων στη διατομή όπως εξάγονται από αεροελαστικους υπολογισμούς. Για πρώτη φορά σε αυτή την εργασία, πραγματοποιήθηκε η στοχαστική ανάλυση ενός τόσο λεπτομερειακού μοντέλου. Ωστόσο η παραπάνω προσέγγιση αποδείχτηκε αρκετά χρονοβόρα. Για το σκοπό αυτό αναπτύχθηκε υπολογιστικό εργαλείο ικανό να εκτελεί ένα μεγάλο αριθμό επαναλήψεων της προαναφερθείσας μεθοδολογίας και να φανεί χρήσιμο στο σχεδιασμό πτερυγίων με προκαθορισμένο επίπεδο αξιοπιστίας. Εξαιτίας της απλότητας της προετοιμασίας των δεδομένων εισόδου και της ταχύτητας επίλυσης, το νέο εργαλείο έδωσε τη δυνατότητα για τη μελέτη διαφόρων στατιστικών υποθέσεων που αφορούσαν τη δομική αξιοπιστία του πτερυγίου εξετάζοντας απευθείας τον δείκτη αξιοπιστίας β της κατασκευής.

碩士
國立臺中教育大學
教育測驗統計研究所
95
The purpose of this study is to analyze the individualized hierarchical structures of fraction addition concepts for sixth graders in Taiwan by using the fuzzy approach of interpretive structural model (FAISM). The researcher first tested 985 sixth graders of elementary schools by using self-designed fraction addition test. Secondly, the researcher analyzed the raw datum through FAISM based on Fuzzy Logic Model of Perception (FLMP), Item Response Theory (IRT) and the algorithm of Interpretive Structural Model (ISM) of fuzzy alpha-cut. Thirdly, the researcher used FAISM software to get the individualized hierarchical structures of fraction addition concepts of high, middle and low-ability examinees. Finally, the researcher compared qualitively and quantitatively about the differences of the individualized hierarchical structures of fraction addition concepts among high, middle, low-ability examinees and the experts. Through the procedures of the analysis, the following conclusions were found. 1. The FAISM was a feasible way for analyzing the concepts structures of fraction addition. 2. The ISM graphs of examinees varied based on different abilities. 3. The concept structures in each item varied greatly with different-ability examinees. 4. According to individualized ISM graphs of fraction addition concepts, the links among concepts could be as references for group teaching and remedial instruction. 5. Based on the referenced standard of experts’ concept structures, the similarity indices of the ISM graphs of examinees with different-ability were significantly different. 6. The similarity indices of ISM graphs between high-ability examinees and experts were not significantly different. But the similarity indices of ISM graphs between middle-ability examinees and experts were significantly different as well as between low-ability examinees and experts. The findings of this study should be helpful for understanding the learning process of fraction addition concepts and as references for remedial instruction or group teaching. Finally, some recommendations and suggestions for future research are provided.

In the Canadian Prairies recurring droughts are one of the realities which can have significant economical, environmental, and social impacts. For example, droughts in 1997 and 2001 cost over $100 million on different sectors. Drought frequency analysis is a technique for analyzing how frequently a drought event of a given magnitude may be expected to occur. In this study the state of the science related to frequency analysis of droughts is reviewed and studied. The main contributions of this thesis include development of a model in Matlab which uses the qualities of Fuzzy C-Means (FCMs) clustering and corrects the formed regions to meet the criteria of effective hydrological regions. In FCM each site has a degree of membership in each of the clusters. The algorithm developed is flexible to get number of regions and return period as inputs and show the final corrected clusters as output for most case scenarios. While drought is considered a bivariate phenomena with two statistical variables of duration and severity to be analyzed simultaneously, an important step in this study is increasing the complexity of the initial model in Matlab to correct regions based on L-comoments statistics (as apposed to L-moments). Implementing a reasonably straightforward approach for bivariate drought frequency analysis using bivariate L-comoments and copula is another contribution of this study. Quantile estimation at ungauged sites for return periods of interest is studied by introducing two new classes of neural network and machine learning: Radial Basis Function (RBF) and Support Vector Machine Regression (SVM-R). These two techniques are selected based on their good reviews in literature in function estimation and nonparametric regression. The functionalities of RBF and SVM-R are compared with traditional nonlinear regression (NLR) method. As well, a nonlinear regression with regionalization method in which catchments are first regionalized using FCMs is applied and its results are compared with the other three models. Drought data from 36 natural catchments in the Canadian Prairies are used in this study. This study provides a methodology for bivariate drought frequency analysis that can be practiced in any part of the world.

In the first part of the dissertation, a novel stochastic averaging technique based on a Hilbert transform definition of the oscillator response displacement amplitude is developed. In comparison to standard stochastic averaging, the requirement of “a priori” determination of an equivalent natural frequency is bypassed, yielding flexibility in the ensuing analysis and potentially higher accuracy. Further, the herein proposed Hilbert transform based stochastic averaging is adapted for determining the time-dependent survival probability and first-passage time probability density function of stochastically excited nonlinear oscillators, even endowed with fractional derivative terms. To this aim, a Galerkin scheme is utilized to solve approximately the backward Kolmogorov partial differential equation governing the survival probability of the oscillator response. Next, the potential of the stochastic averaging technique to be used in conjunction with performance-based engineering design applications is demonstrated by proposing a stochastic version of the widely used incremental dynamic analysis (IDA). Specifically, modeling the excitation as a non-stationary stochastic process possessing an evolutionary power spectrum (EPS), an approximate closed-form expression is derived for the parameterized oscillator response amplitude probability density function (PDF). In this regard, IDA surfaces are determined providing the conditional PDF of the engineering demand parameter (EDP) for a given intensity measure (IM) value. In contrast to the computationally expensive Monte Carlo simulation, the methodology developed herein determines the IDA surfaces at minimal computational cost. In the second part of the dissertation, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Several numerical examples are considered for assessing the reliability of the technique, even in the presence of incomplete and corrupted data. These include a 2-DOF time-variant Duffing oscillator endowed with fractional derivative terms, as well as a 2-DOF system subject to flow-induced forces where the non-stationary sea state possesses a recently proposed evolutionary version of the JONSWAP spectrum. In the third part of this dissertation, a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) is developed for dynamic cerebral autoregulation (DCA) performance quantification. DCA is the continuous counter-regulation of the cerebral blood flow by the active response of cerebral blood vessels to the spontaneous or induced blood pressure fluctuations. Specifically, various metrics of the phase shift and magnitude of appropriately defined GHW-based transfer functions are determined based on data points over the joint time-frequency domain. The potential of these metrics to be used as a diagnostics tool for indicating healthy versus impaired DCA function is assessed by considering both healthy individuals and patients with unilateral carotid artery stenosis. Next, another application in biomedical engineering is pursued related to the Pulse Wave Imaging (PWI) technique. This relies on ultrasonic signals for capturing the propagation of pressure pulses along the carotid artery, and eventually for prognosis of focal vascular diseases (e.g., atherosclerosis and abdominal aortic aneurysm). However, to obtain a high spatio-temporal resolution the data are acquired at a high rate, in the order of kilohertz, yielding large datasets. To address this challenge, an efficient data compression technique is developed based on the multiresolution wavelet decomposition scheme, which exploits the high correlation of adjacent RF-frames generated by the PWI technique. Further, a sparse matrix decomposition is proposed as an efficient way to identify the boundaries of the arterial wall in the PWI technique.

The analysis of vehicle-structure interaction systems plays a significant role in the design and maintenance of bridges. In recent years, the assessment of the health of existing bridges and the design of new ones has gained significance, in part due to the progress made in the development of faster moving locomotives, the desire for lighter bridges, and the imposition of performance criteria against rare events such as occurrence of earthquakes and fire. A probabilistic analysis would address these issues, and also assist in determination of reliability and in estimating the remaining life of the structure. In this thesis, we aim to develop tools for the probabilistic analysis techniques of state estimation, parameter identification and global response sensitivity analysis of vehicle-structure interaction systems, which are also applicable to the broader class of structural dynamical systems. The thesis is composed of six chapters and three appendices. The contents of these chapters and the appendices are described in brief in the following paragraphs. In chapter 1, we introduce the problem of probabilistic analysis of vehicle-structure interactions. The introduction is organized in three parts, dealing separately with issues of forward problems, inverse problems, and global response sensitivity analysis. We begin with an overview of the modelling and analysis of vehicle-structure interaction systems, including the application of spatial substructuring and mesh partitioning schemes. Following this, we describe Bayesian techniques for state and parameter estimation for the general class of state-space models of dynamical systems, including the application of the Kalman filter and particle filters for state estimation, MCMC sampling based filters for parameter identification, and the extended Kalman filter, the unscented Kalman filter and the ensemble Kalman filter for the problem of combined state and parameter identification. In this context, we present the Rao-Blackwellization method which leads to variance reduction in particle filtering. Finally, we present the techniques of global response sensitivity analysis, including Sobol’s analysis and distance-based measures of sensitivity indices. We provide an outline and a review of literature on each of these topics. In our review of literature, we identify the difficulties encountered when adopting these tools to problems involving vehicle-structure interaction systems, and corresponding to these issues, we identify some open problems for research. These problems are addressed in chapters 2, 3, 4 and 5. In chapter 2, we study the application of finite element modelling, combined with numerical solutions of governing stochastic differential equations, to analyse instrumented nonlinear moving vehicle-structure systems. The focus of the chapter is on achieving computational efficiency by deploying, within a single modeling framework, three sub structuring schemes with different methodological moorings. The schemes considered include spatial substructuring schemes (involving free-interface coupling methods), a spatial mesh partitioning scheme for governing stochastic differential equations (involving the use of a predictor corrector method with implicit integration schemes for linear regions and explicit schemes for local nonlinear regions), and application of the Rao-Blackwellization scheme (which permits the use of Kalman’s filtering for linear substructures and Monte Carlo filters for nonlinear substructures). The main effort in this work is expended on combining these schemes with provisions for interfacing of the substructures by taking into account the relative motion of the vehicle and the supporting structure. The problem is formulated with reference to an archetypal beam and multi-degrees of freedom moving oscillator with spatially localized nonlinear characteristics. The study takes into account imperfections in mathematical modelling, guide way unevenness, and measurement noise. The numerical results demonstrate notable reduction in computational effort achieved on account of introduction of the substructuring schemes. In chapter 3, we address the issue of identification of system parameters of structural systems using dynamical measurement data. When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. In this chapter, strategies are proposed based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples include a laboratory study on a beam-moving trolley system. In chapter 4, we consider the combined estimation of the system states and parameters of vehicle-structure interaction systems. To this end, we formulate a framework which uses MCMC sampling for parameter estimation and particle filtering for state estimation. In chapters 2 and 3, we described the computational issues faced when adopting these techniques individually. When used together, we come across both sets of issues, and find the complexity of the estimation problem is greatly increased. In this chapter, we address the computational issues by adopting the sub structuring techniques proposed in chapter 2, and the parameter identification method based on modified measurement models presented in chapter 3. The proposed method is illustrated on a computational study on a beam-moving oscillator system with localized nonlinearities, as well as on a laboratory study on a beam-moving trolley system. In chapter 5, we present global response sensitivity indices for structural dynamical systems with random system parameters excited by multiple random excitations. Two new procedures for evaluating global response sensitivity measures with respect to the excitation components are proposed. The first procedure is valid for stationary response of linear systems under stationary random excitations and is based on the notion of Hellinger’s metric of distance between two power spectral density functions. The second procedure is more generally valid and is based on the l2 norm based distance measure between two probability density functions. Specific cases which admit exact solutions are presented and solution procedures based on Monte Carlo simulations for more general class of problems are outlined. The applicability of the proposed procedures to the case of random system parameters is demonstrated using suitable illustrations. Illustrations include studies on a parametrically excited linear system and a nonlinear random vibration problem involving moving oscillator-beam system that considers excitations due to random support motions and guide-way unevenness. In chapter 6 we summarize the contributions made in chapters 2, 3, 4, and 5, and on the basis of these studies, present a few problems for future research. In addition to these chapters, three appendices are included in this thesis. Appendices A and B correspond to chapter 3. In appendix A, we study the effect on the nature of the posterior probability density functions of large measurement data set and small measurement noise. Appendix B illustrates the MCMC sampling based parameter estimation procedure of chapter 3 using a laboratory study on a bending–torsion coupled, geometrically non-linear building frame under earthquake support motion. In appendix C, we present Ito-Taylor time discretization schemes for stochastic delay differential equations found in chapter 5.

碩士
國立臺中教育大學
教育測驗統計研究所
96
The purpose of this study is to use fuzzy approach interpretive structural model (FAISM) in analyzing concept structure of mathematics indicators on number and quantity for second graders. This method integrates algorithm of fuzzy logic model of perception (FLMP) and interpretive structural model (ISM). The combined algorithm of this integrated model could analyze the individualized concept structure based on the comparisons with expert. There are totally 979 second graders in this study. The paper-pencil test on number and quantity is designed by the researcher. By using the FAISM software, we can get the diagram of individualized concept structure. The results of this study are as follows. 1.Examinees with different ability own varied ISM diagrams. 2.Examinees with the same total score but different response patterns own varied ISM diagrams. 3.Examinees of different clusters own varied ISM diagrams. 4.The similarity coefficients of ISM diagrams are both significantly different among examinees of different clusters and different ability. 5.Based on the comparisons with expert, examinees of different clusters and different ability have significantly different similarity coefficients. The results of this study can be provided as the references for cognition diagnosis, remedial teaching and courses design. At last, based on the findings and results, some suggestions and recommendations for future research are provided.