Infrastructure systems are crucial facilities. They supply the necessary transportation, water and energy utilities for the public. However, while aging, these systems gradually deteriorate in time and approach the end of their lifespans. As a result, they require periodic maintenance and repair in order to function and be reliable throughout their lifetimes. Bridge infrastructure is an essential part of the transportation infrastructure. Bridge management systems (BMSs), used to monitor the condition and safety of the bridges in a bridge infrastructure, have evolved considerably in the past decades. The aim of BMSs is to use the resources in an optimal manner keeping the bridges out of risk of failure. The BMSs use the lifetime performance curves to predict the future condition of the bridge elements or bridges. The most widely implemented condition-based performance prediction and maintenance optimization model is the Markov Decision Process-based models (MDP). The importance of the Markov Decision Process-based model is that it defines the time-variant deterioration using the Markov Transition Probability Matrix and performs the lifetime cost optimization by finding the optimum maintenance policy. In this study, the Markov decision process-based model is examined and a computer program to find the optimal policy with discounted life-cycle cost is developed. The other performance prediction model investigated in this study is a probabilistic Bi-linear model which takes into account the uncertainties for the deterioration process and the application of maintenance actions by the use of random variables. As part of the study, in order to further analyze and develop the Bi-linear model, a Latin Hypercube Sampling-based (LHS) simulation program is also developed and integrated into the main computational algorithm which can produce condition, safety, and life-cycle cost profiles for bridge members with and without maintenance actions. Furthermore, a polynomial-based condition prediction is also examined as an alternative performance prediction model. This model is obtained from condition rating data by applying regression analysis. Regression-based performance curves are regenerated using the Latin Hypercube sampling method. Finally, the results from the Markov chain-based performance prediction are compared with Simulation-based Bi-linear prediction and the derivation of the transition probability matrix from simulated regression based condition profile is introduced as a newly developed approach. It has been observed that the results obtained from the Markov chain-based average condition rating profiles match well with those obtained from Simulation-based mean condition rating profiles. The result suggests that the Simulation-based condition prediction model may be considered as a potential model in future BMSs.

Pagrindinis šio darbo tikslas yra sukurti daugiapakopių procesų būsenų modelį, kuriuo būtų galima modeliuoti įvairių galimų bet kokios sistemos trikdžių scenarijus ir atlikti demonstracinius skaičiavimus. Atsiradus sutrikimui ar pažeidimams sutrikdomas kitų sistemoje dalyvaujančių pakopų darbas ir turime tam tikras pasekmes, kurios iššaukia problemas, liečiančias aplinkui funkcionuojančius sektorius. Todėl yra labai svarbu nustatyti daugiapakopių procesų būsenų modelio galimų būsenų scenarijus, išanalizuoti jų tikėtinumą bei dažnumą ir įvertinti. Daugiausiai dėmesio skiriama perėjimo tikimybių iš vienos pakopos būsenų į kitos pakopos būsenas matricų modeliavimui ir skaičiavimo algoritmo kūrimui. Tada atliekame stebėjimą kaip elgiasi trikdžių pasirodymo tikimybės per 100 perėjimų. Tam naudojami Markovo grandinės bei procesai ir tikimybiniai skirstiniai. / The main purpose of this research is to develop multi-stage process states model that could simulate a possible range of any system failures and demonstrational calculations. In the event of disruption or irregularities affects the other systems involved in stage work and we have certain consequences, which triggered concerns about the functioning around the sector. It is very important to establish a multi-stage process states model, the possible states of scenarios, analyze their probability and the frequency and to assess it. Focuses on the transition probabilities between states in the next tier level status matrix modeling and computing algorithm. Then perform the behavior tracking script and the likelihood of interference, the likelihood of the appearance of over 100 transitions. For this purpose, Markov chains and processes, and probabilistic distributions are used.

We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.

A scheme, analogous to the linear combination of atomic orbitals (LCAO), is used to calculate rates of reactions for the fusion of nuclei con¯ned in molecules. As an example, the possibility of nuclear fusion in rotationally excited H2O molecules of angular momentum 1¡ is estimated for the p + p + 16O ! 18Ne¤(4:522; 1¡) nuclear transition. Due to a practically exact agreement of the energy of the Ne resonance and of the p + p + 16O threshold, the possibility of an enhanced transition probability is investigated. / Physics / M.Sc.

A credit card as a banking product has a dual nature both as a convenient loan and a payment tool. Credit card profitability prediction is a complex problem because of the variety of the card holders' behaviour patterns, a fluctuating balance, and different sources of interest and transactional income. The state of a credit card account depends on the type of card usage and payments delinquency, and can be defined as inactive, transactor, revolver, delinquent, and default. The proposed credit cards profit prediction model consists of four stages: i) utilisation rate and interest rate income prediction, ii) non-interest rate income prediction, iii) account state prediction with conditional transition probabilities, and iv) the aggregation of the partial models into total income estimation. This thesis describes an approach to credit card account-level profitability prediction based on multistate and multistage conditional probabilities models with different types of income and compares methods for the most accurate predictions. We use application, behavioural, card state, and macroeconomic characteristics as predictors. This thesis contains nine chapters: Introduction, Literature Review, six chapters giving descriptions of the data, methodologies and discussions of the results of the empirical investigation, and Conclusion. Introduction gives the key points and main aims of the current research and describes the general schema of the total income prediction model. Literature Review proposes a systematic analysis of academic work on loan profit modelling and highlights the gaps in the application of profit scoring to credit cards income prediction. Chapter 3 describes the data sample and gives the overview of characteristics. Chapter 4 is dedicated to the prediction of the credit limit utilisation and contains the comparative analysis of the predictive accuracy of different regression models. We apply five methods such as i) linear regression, ii) fractional regression, iii) beta-regression, iv) beta-transformation, and v) weighted logistic regression with data binary transformation for utilisation rate prediction for one- and two-stage models. Chapters 5 and 6 are dedicated to modelling the transition probabilities between credit card states. Chapter 5 describes the general model setups, model building methodology such as transition probability prediction with conditional binary logistic, ordinal, and multinomial regressions, the data sample description, the univariate analysis of predictors. Chapter 6 discusses regression estimation results for all types of regression and a comparative analysis of the models. Chapter 7 describes an approach to the non-interest rate income prediction and contains a comparative analysis of panel data regression techniques such as pooled and four random effect methods. We consider two sources of non-interest income generation: i) interchange fees and foreign exchange fees from transactions via pointof- sales (POS) and ii) ATM fees from cash withdrawals. We compare the predictive accuracy of a one-stage approach, which means the usage of a single linear model for the income amount estimation, and a two-stage approach, which means that the income amount conditional on the probability of POS and ATM transaction. Chapter 8 aggregates the results from the partial models into a single model for total income estimation. We assume that a credit card account does not have a single particular state and a single behavioural type in the future, but has a chance to move to any of possible states. The income prediction model is selected according to these states, and the transition probabilities are used as weights for the particular interest rate and non-interest rate income prediction models. Conclusion highlights the contributions of this research. We propose an innovative methodological approach for credit card income prediction as a system of models, which considers the estimation of the income from different sources and then aggregates the income estimations weighted by the states transition probabilities. The results of comparative analysis of regression methods for: i) utilization rate of credit limit and ii) non-interest income prediction, iii) the use of panel data with pooled and random effect for profit scoring, and iv) account level non-binary target transition probabilities estimation for credit cards can be used as benchmarks for further research and fill the gaps of empirical investigations in the literature. The estimation of the transition probability between states at the account level helps to avoid the memorylessness property of the Markov Chains approach. We have investigated the significance of predictors for models of this type. The proposed modelling approach can be applied for the development of business strategies such as credit limit management, customer segmentation by the profitability and behavioural type.

We consider a longitudinal system in which transitions between the states are governed by a discrete time finite state space stochastic process X. Our aim, using aggregated sample survey data of the form typically collected by official statistical agencies, is to undertake model based inference for the underlying process X. We will develop inferential techniques for continuing sample surveys of two distinct types. First, longitudinal surveys in which the same individuals are sampled in each cycle of the survey. Second, cross-sectional surveys which sample the same population in successive cycles but with no attempt to track particular individuals from one cycle to the next. Some of the basic results have appeared in Davis et al (2001) and Davis et al (2002).¶ Longitudinal surveys provide data in the form of transition frequencies between the states of X. In Chapter Two we develop a method for modelling and estimating the one-step transition probabilities in the case where X is a non-homogeneous Markov chain and transition frequencies are observed at unit time intervals. However, due to their expense, longitudinal surveys are typically conducted at widely, and sometimes irregularly, spaced time points. That is, the observable frequencies pertain to multi-step transitions. Continuing to assume the Markov property for X, in Chapter Three, we show that these multi-step transition frequencies can be stochastically interpolated to provide accurate estimates of the one-step transition probabilities of the underlying process. These estimates for a unit time increment can be used to calculate estimates of expected future occupation time, conditional on an individual’s state at initial point of observation, in the different states of X.¶ For reasons of cost, most statistical collections run by official agencies are cross-sectional sample surveys. The data observed from an on-going survey of this type are marginal frequencies in the states of X at a sequence of time points. In Chapter Four we develop a model based technique for estimating the marginal probabilities of X using data of this form. Note that, in contrast to the longitudinal case, the Markov assumption does not simplify inference based on marginal frequencies. The marginal probability estimates enable estimation of future occupation times (in each of the states of X) for an individual of unspecified initial state. However, in the applications of the technique that we discuss (see Sections 4.4 and 4.5) the estimated occupation times will be conditional on both gender and initial age of individuals.¶ The longitudinal data envisaged in Chapter Two is that obtained from the surveillance of the same sample in each cycle of an on-going survey. In practice, to preserve data quality it is necessary to control respondent burden using sample rotation. This is usually achieved using a mechanism known as rotation group sampling. In Chapter Five we consider the particular form of rotation group sampling used by the Australian Bureau of Statistics in their Monthly Labour Force Survey (from which official estimates of labour force participation rates are produced). We show that our approach to estimating the one-step transition probabilities of X from transition frequencies observed at incremental time intervals, developed in Chapter Two, can be modified to deal with data collected under this sample rotation scheme. Furthermore, we show that valid inference is possible even when the Markov property does not hold for the underlying process.

This thesis presents a comprehensive example framework on how current multiple model state estimation algorithms for jump Markov linear systems can be improved. The possible improvements are categorized as: -Design of multiple model state estimation algorithms using new criteria. -Improvements obtained using existing multiple model state estimation algorithms. In the first category, risk-sensitive estimation is proposed for jump Markov linear systems. Two types of cost functions namely, the instantaneous and cumulative cost functions related with risk-sensitive estimation are examined and for each one, the corresponding multiple model estate estimation algorithm is derived. For the cumulative cost function, the derivation involves the reference probability method where one defines and uses a new probability measure under which the involved processes has independence properties. The performance of the proposed risk-sensitive filters are illustrated and compared with conventional algorithms using simulations. The thesis addresses the second category of improvements by proposing -Two new online transition probability estimation schemes for jump Markov linear systems. -A mixed multiple model state estimation scheme which combines desirable properties of two different multiple model state estimation methods. The two online transition probability estimators proposed use the recursive Kullback-Leibler (RKL) procedure and the maximum likelihood (ML) criteria to derive the corresponding identification schemes. When used in state estimation, these methods result in an average error decrease in the root mean square (RMS) state estimation errors, which is proved using simulation studies. The mixed multiple model estimation procedure which utilizes the analysis of the single Gaussian approximation of Gaussian mixtures in Bayesian filtering, combines IMM (Interacting Multiple Model) filter and GPB2 (2nd Order Generalized Pseudo Bayesian) filter efficiently. The resulting algorithm reaches the performance of GPB2 with less Kalman filters.

We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

A scheme, analogous to the linear combination of atomic orbitals (LCAO), is used to calculate rates of reactions for the fusion of nuclei con¯ned in molecules. As an example, the possibility of nuclear fusion in rotationally excited H2O molecules of angular momentum 1¡ is estimated for the p + p + 16O ! 18Ne¤(4:522; 1¡) nuclear transition. Due to a practically exact agreement of the energy of the Ne resonance and of the p + p + 16O threshold, the possibility of an enhanced transition probability is investigated. / Physics / M.Sc.