Abstract There are gradually prosperous trades in foreign exchange markets, agents could hedge, speculate and arbitrage in markets. Market efficiency therefore is worthy of investigate in international finance. There are a lot of empirical studies examine whether the long-run relationship would exist between spot exchange rate and forward exchange rate in conventional linear models. However the conclusions were not similar. Sarno and Chowdhury¡]2003¡^mentioned that linear models imply residuals of model adjust to equilibrium by fixed speed. If dynamic adjustment of nonlinear model exists, linear model is hard to capture the dynamic adjustment. Ender¡]1995¡^also mentioned that cointegration has long run linear relationship in variables. Theoretically, nonlinear relationship may exist. Furthermore, some literatures demonstrate how transaction cost and technical analysis induce nonlinear adjustment of the deviation for equilibrium exchange rate. We consider a new approach that Tersävirta and Anderson¡]1992¡^provided the Smooth Transition Autoregressive Model¡]STAR¡^, to re-examine the long-run relationship between spot exchange rate and forward exchange rate. According to the empirical results, we can find that all variables can be modeled by nonlinear models. The results of relationships exist between spot and forward exchange rates in France, Germany, Canada, Japan, Norway, Spain, Australia, Ireland, Italy, .Austria, Belgium, Denmark, Luxembourg, the Netherlands, Sweden, Switzerland, Greece and New Zealand, but it doesn¡¦t exist in the United Kingdom and Finland.

This thesis includes two topics. The first one is the architecture as well as the circuit implementation of an ultra low-power direct digital frequency synthesizer (DDFS) based on the straight line approximation. The second one is the circuit implementation of the low-power DDFS with an error compensation. The proposed approximation technique replaces the conventional ROM-based phase-to-amplitude conversion circuitry and the linear digital-to-analog converter with a nonlinear digital-to-analog converter (DAC) to realize a simple approximation of the sine function. Thus, the overall power dissipation as well as hardware complexity can be significantly reduced. Besides, by adding the error compensation, the spurious-free dynamic range (SFDR) of the synthesized output signal can be raised drastically.

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­^¤åºK­n A time-independent finite-difference numerical scheme is developed to study the dynamic response of a submerged and a floating breakwater under the wave loading of a fully numerical force. The coupled surge, heave and pitch motion of a floating breakwater and the wave-structure interaction are included in the model. The numerical results are validated uses several bench mark studies and results available elsemlse. The wave reducing effect of a submerged and a floating breakwaters were analysis and discusse.

In principle, general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach. The central idea to this recur- sive Bayesian estimation is to determine the probability density function of the state vector of the nonlinear systems conditioned on the available measurements. However, the optimal exact solution to this Bayesian filtering problem is intractable since it requires an infinite dimensional process. For practical nonlinear filtering applications approximate solutions are required. Recently efficient and accurate approximate non- linear filters as alternatives to the extended Kalman filter are proposed for recursive nonlinear estimation of the states and parameters of dynamical systems. First, as sampling-based nonlinear filters, the sigma point filters, the unscented Kalman fil- ter and the divided difference filter are investigated. Secondly, a direct numerical nonlinear filter is introduced where the state conditional probability density is calcu- lated by applying fast numerical solvers to the Fokker-Planck equation in continuous- discrete system models. As simulation-based nonlinear filters, a universally effective algorithm, called the sequential Monte Carlo filter, that recursively utilizes a set of weighted samples to approximate the distributions of the state variables or param- eters, is investigated for dealing with nonlinear and non-Gaussian systems. Recentparticle filtering algorithms, which are developed independently in various engineer- ing fields, are investigated in a unified way. Furthermore, a new type of particle filter is proposed by integrating the divided difference filter with a particle filtering framework, leading to the divided difference particle filter. Sub-optimality of the ap- proximate nonlinear filters due to unknown system uncertainties can be compensated by using an adaptive filtering method that estimates both the state and system error statistics. For accurate identification of the time-varying parameters of dynamic sys- tems, new adaptive nonlinear filters that integrate the presented nonlinear filtering algorithms with noise estimation algorithms are derived. For qualitative and quantitative performance analysis among the proposed non- linear filters, systematic methods for measuring the nonlinearities, biasness, and op- timality of the proposed nonlinear filters are introduced. The proposed nonlinear optimal and sub-optimal filtering algorithms with applications to spacecraft orbit es- timation and autonomous navigation are investigated. Simulation results indicate that the advantages of the proposed nonlinear filters make these attractive alterna- tives to the extended Kalman filter.

A new construction of regular solutions to the three dimensional Navier{Stokes equa- tions is introduced and applied to the study of their asymptotic expansions. This construction and other Phragmen-Linderl??of type estimates are used to establish su??- cient conditions for the convergence of those expansions. The construction also de??nes a system of inhomogeneous di??erential equations, called the extended Navier{Stokes equations, which turns out to have global solutions in suitably constructed normed spaces. Moreover, in these spaces, the normal form of the Navier{Stokes equations associated with the terms of the asymptotic expansions is a well-behaved in??nite system of di??erential equations. An application of those asymptotic expansions of regular solutions is the analysis of the helicity for large times. The dichotomy of the helicity's asymptotic behavior is then established. Furthermore, the relations between the helicity and the energy in several cases are described.

In chemical processes, online measurements of all the process variables and parameters required for process control, monitoring and optimization are seldom available. The use of soft sensors or observers is, therefore, highly significant as they can estimate unmeasured state variables from available process measurements. However, for reliable estimation by a soft sensor, the process measurements have to be placed at locations that allow reconstruction of process variables by the soft sensors. This dissertation presents a new technique for computing an optimal measurement structure for state and parameter estimation of stable nonlinear systems. The methodology can compute locations for individual sensors as well as networks of sensors where a trade-off between process information, sensor cost, and information redundancy is taken into account. The novel features of the approach are (1) that the nonlinear behavior that a process can exhibit over its operating region can be taken into account, (2) that the technique is applicable for systems described by lumped or by distributed parameter models, (3) that the technique reduces to already established methods, if the system is linear and only some of the objectives are examined, (4) that the results obtained from the procedure can be easily interpreted, and (5) that the resulting optimization problem can be decomposed, resulting in a significant reduction of the computational effort required for its solution. The other issue addressed in this dissertation is designing soft sensors for a given measurement structure. In case of high-dimensional systems, the application of conventional soft sensor or observer designs may not always be practical due to the high computational requirements or the resulting observers being too sensitive to measurement noise. To address these issues, this dissertation presents reduced-order observer design techniques for state estimation of high-dimensional chemical processes. The motivation behind these approaches is that subspaces, which are close to being unobservable, cannot be correctly reconstructed in a realistic setting due to measurement noise and inaccuracies in the model. The presented approaches make use of this observation and reconstruct the parts of the system where accurate state estimation is possible.

Magnetic bearings use variable attractive forces generated by electromagnetic control coils to support rotating shafts with low friction and no material wear while providing variable stiffness and damping. Rotor deflections are stabilized by position feedback control along two axes using non-contacting displacement sensors. These sensor signals contain sensor runout error which can be represented by a Fourier series composed of harmonics of the spin frequency. While many methods have been proposed to compensate for these runout harmonics, most are computationally intensive and can destabilize the feedback loop. One attractive alternative is to increase the number of displacement sensors and map individual probe voltages to the two independent control signals. This approach is implemented using a circular sensor array and single weighting gain matrix in the present work. Analysis and simulations show that this method eliminates runout harmonics from 2 to n-2 when all sensors in an ideal n-sensor array are operational. Sensor failures result in reduced synchronous amplitude and increased harmonic amplitudes after failure. These amplitudes are predicted using derived expressions and synchronous measurement error can be corrected using an adjustment factor for single failures. A prototype 8-sensor array shows substantial runout reduction and bandwidth and sensitivity comparable to commercial systems. Nonlinear behavior in homopolar magnetic bearings is caused primarily by the quadratic relationship between coil currents and magnetic support forces. Governing equations for a permanent magnet biased homopolar magnetic bearing are derived using magnetic circuit equations and linearized using voltage and position stiffness terms. Nonlinear hardening and softening spring behavior is achieved by varying proportional control gain and frequency response is determined for one case using numerical integration and a shooting algorithm. Maximum amplitudes and phase reversal for this nonlinear system occur at lower frequencies than the linearized system. Rotor oscillations exhibit amplitude jumps by cyclic fold bifurcations, creating a region of hysteresis where multiple stable equilibrium states exist. One of these equilibrium states contains subharmonic frequency components resulting in quasiperiodic rotor motion. This nonlinear analysis shows how nonlinear rotor oscillations can be avoided for a wide range of operation by careful selection of design parameters and operating conditions.