Writers on the business cycle often emphasize that non-linear models are needed to account for certain of its features. Thus it is often said that either the asymmetry of the duration of business cycle expansions and contractions or the variability of these quantities demand a non-linear model. Such comments are rarely made precise however and mostly consist of references to such assertions from the past. Thus the asymmetry in the cycle is mostly accompanied by references to Keynes (1936) and Burns and Mitchell (1946). But these authors were looking at what we call today the classical cycle i.e. movements in the level of GDP, and so the fact that there are long expansions and short contractions can arise simply due to the presence of long-run growth in the economy, and it is not obvious that it has much to do with non-linearity. This thesis aims to introduce various statistics that can be used to characterise the specific shape of the non-linearity observed in macroeconomic time series. Chapter 2 introduces a range of statistics and presents the dating algorithm used in this thesis, which is based on the BBQ algorithm of Harding and Pagan (2002). Chapter 3 tests the adequacy of linear models versus the SETAR model of van Dijk and Franses(2003) and the bounceback model of Kim, Morley and Piger (2005) in capturing observed non-linear features of the data. Chapter 4 extends this work by examining the three state Markov model of Hamilton (1989), again using the ??bounce-back?? model of Kim C., Morley, J. and J. Piger, (2005), and the more complicated ??tension?? model of DeJong, D., Dharmarajan, H., Liesenfeld, R. and Richard, J., (2005). Chapter 4 also extends Chapter 3 by estimating the above mentioned models on US GDP, Australian non-farm GDP, US investment and Australian dwellings investment. They are then simulated in order to gauge the cycle properties. Chapter 5 analyses the business cycle implications of two related multivariate dynamic factor models presented in papers by Kim and Piger (2001, 2002). Finally Chapter 6 concludes.

With the growth in importance of the aluminium industry, has come increased demand to invest into the quality improvement of the different aluminium based hot extruded products. One of the main mechanisms, which can influence deformation at high temperature within the 6xxx aluminium, is linked to the presence of the AlFeSi intermetallic phases. These phases severely restrict hot workability when present as hard and brittle plate-like precipitates b-AlFeSi. Damage initiation occurs in these alloys by decohesion or fracture of these intermetallic inclusions. The understanding and modeling of the deformation and fracture behavior of aluminium alloys at room and at hot working temperature is very important for optimizing manufacturing processes such as extrusion. The ductility of 6xxx aluminium alloys can be directly related to chemical composition and to the microstructural evolution occurring during the heat treatment procedures preceding extrusion if proper physics based deformation and fracture models are used. In this thesis, room temperature and hot tensile tests are adopted to address the problem experimentally. The damage evolution mechanisms is defined at various temperatures and a micromechanics based model of the Gurson type considering several populations of cavities nucleated by different second phase particles groups is developed on the basis of the experimental observations. This model allows relating quantitatively microstructure and ductility at various temperatures strain rates and stress triaxialities. Finite element simulations based on an enhanced micromechanics-based model are used to validate the model. Finally, the effect of some key factors that determine the extrudability of aluminium is also discussed and a correlation between the ductility calculations in uniaxial tension and the maximum extrusion speed is developed for one defined profile.

Constraint modeling could be a very important system validation method, because its abilities are complementary to both testing and code inspection. In particular, even though the ability of constraint modeling to find errors is limited by the simplifications which are introduced when making a constraint model, constraint modeling can locate important classes of errors which are caused by non-local faults (i.e., are hard to find with code inspection) and manifest themselves as failures only in unusual situations (i.e., are hard to find with testing).

This thesis presents the development of hardware, theory, and experimental methods to enable a robotic manipulator arm to interact with soils and estimate soil properties from interaction forces. Unlike the majority of robotic systems interacting with soil, our objective is parameter estimation, not excavation. To this end, we design our manipulator with a flat plate for easy modeling of interactions. By using a flat plate, we take advantage of the wealth of research on the similar problem of earth pressure on retaining walls. There are a number of existing earth pressure models. These models typically provide estimates of force which are in uncertain relation to the true force. A recent technique, known as numerical limit analysis, provides upper and lower bounds on the true force. Predictions from the numerical limit analysis technique are shown to be in good agreement with other accepted models. Experimental methods for plate insertion, soil-tool interface friction estimation, and control of applied forces on the soil are presented. In addition, a novel graphical technique for inverting the soil models is developed, which is an improvement over standard nonlinear optimization. This graphical technique utilizes the uncertainties associated with each set of force measurements to obtain all possible parameters which could have produced the measured forces. The system is tested on three cohesionless soils, two in a loose state and one in a loose and dense state. The results are compared with friction angles obtained from direct shear tests. The results highlight a number of key points. Common assumptions are made in soil modeling. Most notably, the Mohr-Coulomb failure law and perfectly plastic behavior. In the direct shear tests, a marked dependence of friction angle on the normal stress at low stresses is found. This has ramifications for any study of friction done at low stresses. In addition, gradual failures are often observed for vertical tools and tools inclined away from the direction of motion. After accounting for the change in friction angle at low stresses, the results show good agreement with the direct shear values.

Homogeneous Charge Compression Ignition (HCCI) is a promising method for combustion engines to provide a substantial reduction in fuel consumption and formation of both nitrogen oxides and soot pollutants in automotive and stationary engines. Control of HCCI combustion timing is essential for the successful integration of the HCCI concept in real applications. This thesis concentrates on control oriented modeling and experimental study of HCCI combustion for control of ignition timing in HCCI engines. A detailed experimental study of HCCI with over 600 operating points on two different engines is done to characterize the complex relationship among the engine variables, the ignition timing and the exhaust temperature. This leads to identifying regions with distinct patterns of cyclic variation for HCCI ignition timing. In addition, main influential factors on the variations of ignition timing and exhaust temperature in HCCI engines are determined. A dynamic full-cycle physics based Control Oriented Model(COM) is derived from using the experimental data and simulations from an HCCI thermo-kinetic model. The COM is validated with a large number of transient and steady-state experimental points. The validation results show that the COM captures the key HCCI dynamics with a high degree of accuracy for control applications. The COM is computationally efficient and all inputs of the model can be readily measured or estimated on a real engine. This makes the COM simple and fast enough for use as an off-line simulation bed to design and evaluate different strategies for physics-based control of combustion timing in HCCI engines.

Medium and short term mine planning require models of mineral deposits that account for internal geological structures that permit scheduling of mine production at a weekly and monthly production periods. Modified kriging estimation techniques are used for accounting for such geologic structures. However, in the case of simulation, it is strongly linked to the use of sequential Gaussian simulation which has difficulties in reproducing internal geologic patterns. This thesis presents: (1) a set of tools to verify the impact of mean and variance trends in a domain; (2) a methodology for identifying highly variable sub-regions within domains; and (3) a simulation methodology that accounts for the internal structures in the domain required by medium and short term planning. Specifically, the simulation approach consists of: (1) moving the domain to a high dimensional space where the features of the internal structures in the domain are more stationary, (2) simulating the realizations via sequential Gaussian simulation, and (3) projecting the results to the initial dimensional space. / Mining Engineering

In power system studies, some parameters cannot be measured directly by using the currently existing power meters. These power system parameters include the power system Thevenin impedance, harmonic impedances, zero sequence impedance, and the load model parameters. The power systems Thevenin impedance at a load bus is an important parameter for power system planning and operation. The effects of changing the system operation conditions on voltages at the load buses can be easily determined if the power system impedance parameters are known. Moreover, by knowing the Thevenin equivalent parameters, one can calculate the systems voltage stability margin and maximum loadability. The knowledge of power system harmonic impedances is necessary for harmonic mitigation, determination of harmonic limit compliance, prediction of system resonance, and harmonic propagation studies. Moreover, real-time monitoring of the systems harmonic impedances provides significant improvements to the design and operation of active filters. The systems zero sequence impedance at the substation bus is also important information for power system studies. It is used to calculate the different ground fault levels at substations. Furthermore, the loads in power systems play a significant role in power system planning, control, and stability analysis. Having reliable and accurate models of the loads is essential for designing automatic control systems and optimizing their configuration. Obtaining such models has been a challenging problem for power system engineers for decades, especially in the current deregulated market environment. This thesis presents newly developed and verified algorithms for online measurement and monitoring of these power system parameters. The algorithm proposed for monitoring the systems Thevenin, harmonic, and zero sequence impedance parameters, uses the natural variations of the loads connected to the substations. The proposed algorithm for monitoring of load model parameters uses the voltage and current waveforms captured during the operation of the Under Load Tap Change (ULTC) transformers installed in the distribution substations. The proposed algorithms are applied to several field measurements from different substations. The results show that the algorithms fulfill the requirements for the online measurement and monitoring of power system Thevenin, harmonic and zero sequence impedances as well as the load model parameters. / Energy Systems

Animal group formation has often been studied by mathematical biologists through PDE models, producing classical results like traveling and stationary waves. Recently, Eftimie et al. introduced a 1-D PDE model that considers three social interactions between individuals in the relevant neighborhoods, specifically re- pulsion, alignment, and attraction. It takes into account the orientation of the neighbors when consider- ing if they can communicate. This has resulted in exciting new movement behaviors like zig-zag pulses, breathers, and feathers. In this work, we translate the Eftimie model into a Lagrangian implementation. Currently, the results from the Lagrangian formulations show many of the results displayed by Eftimie’s original PDE model, producing patterns like the zig-zag, breather traveling, and stationary pulses. In addi- tion, we model animal movement with an ODE approach to complete the investigation regarding the role of direction-dependent communication mechanism in discrete-space. / Applied Mathematics

Serpentine ducts used by both military and commercial aircraft can generate significant flow angularity (inlet swirl) and total pressure distortion at the engine face. The impact of inlet swirl on the engine performance and operability must be quantified to ensure safe operation of the aircraft and propulsion system and to define installed deficiencies. Testing is performed over a wide range of flight conditions in the propulsion system flight envelope in order to quantify these effects. Turbine engine compressor models are based on experimental data which can be collected at a limited number of discrete operating points. These models can be used as an analysis tool to optimize the engine test plan and help during validation of the design. The Dynamic Turbine Engine Compressor Code (DYNTECC) utilizes parallel compressor theory and quasi-one-dimensional Euler equations to determine compressor performance. In its standard form, DYNTECC uses user-supplied characteristic stage maps in order to calculate stage forces and shaft work for use in the momentum and energy equations. These maps are typically developed using experimental data. These maps can also be created using characteristic codes such as the 1-D Mean Line Code or the 2-D Streamline Curvature Code. The 1-D Mean Line Code was originally created to predict the performance of individual compressor stages and requires greatly reduced computational time when compared to 2-D and 3-D models. This thesis documents work done to incorporate the 1-D Mean Line code into DYNTECC as a subroutine. The combine DYNTECC/1-D Mean Line Code was then used to analyze the effects of inlet swirl on the fan performance and operability of the Honeywell F109 turbofan engine. The code was calibrated and validated using the F109 cycle deck. Additional code validation was performed using experimental data gathered at the United States Air Force Academy. F109 fan maps were developed for various cases of inlet swirl and results were presented showing shifts in corrected mass flow, fan pressure ratio and fan stability limit.

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