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Due to its complex and multidisciplinary nature, the conceptual design phase of helicopters becomes critical in meeting customer satisfaction. Statistical (probabilistic) design methods can be employed to understand the design better and target a design with lower variability. In this thesis, a conceptual design and helicopter sizing methodology is developed and shown on a helicopter design for Turkey.

It has been conventional to simplify the thermo-mechanical modeling of solder joints by omitting the primary (transient) contributions to total creep deformation, assuming that secondary (steady-state) creep strain is dominant and primary creep is negligible. The error associated with this assumption has been difficult to assess because it depends on the properties of the solder joint and the temperature-time profile. This research examines the relative contributions of primary and secondary creep in Sn3.8Ag0.7Cu solder using the constant load creep and stress relaxation measurements for bulk tensile specimens and the finite element analysis of a chip resistor (trilayer) solder joint structure that was thermally cycled under multiple temperature ranges and ramp rates. It was found that neglect of primary creep can result in errors in the predicted stress and strain of the solder joint. In turn, these discrepancies can lead to errors in the estimation of the solder thermal fatigue life due to the changing proportion of primary creep strain to total inelastic strain under different thermal profiles. The constant-load creep and stress relaxation data for Sn3.8Ag0.7Cu span a range of strain rates 10(-8) 1/s < strain rate < 10(-4) 1/s, and temperatures 25°C, 75°C and 100°C. Creep and stress relaxation measurements show that transient creep caused faster strain rates during stress relaxation for a given stress compared to the corresponding minimum creep rate from constant-load creep tests. The extent of strain hardening during primary creep was a function of temperature and strain rate. A constitutive creep model was presented for Sn3.8Ag0.7Cu that incorporates both transient and steady-state creep to provide agreement for both creep and stress relaxation data with a single set of eight coefficients. The model utilizes both temperature compensated time and strain rate to normalize minimum strain rate and saturated transient creep strain, thereby establishing equivalence between decreased temperature and increased strain rate. The apparent activation energy of steady-state creep was indicative of both dislocation core and bulk lattice diffusion was the most sensitive model parameter. A saturation threshold was defined that distinguishes whether primary or secondary creep is dominant under either static or variable loading.

It has been conventional to simplify the thermo-mechanical modeling of solder joints by omitting the primary (transient) contributions to total creep deformation, assuming that secondary (steady-state) creep strain is dominant and primary creep is negligible. The error associated with this assumption has been difficult to assess because it depends on the properties of the solder joint and the temperature-time profile. This research examines the relative contributions of primary and secondary creep in Sn3.8Ag0.7Cu solder using the constant load creep and stress relaxation measurements for bulk tensile specimens and the finite element analysis of a chip resistor (trilayer) solder joint structure that was thermally cycled under multiple temperature ranges and ramp rates. It was found that neglect of primary creep can result in errors in the predicted stress and strain of the solder joint. In turn, these discrepancies can lead to errors in the estimation of the solder thermal fatigue life due to the changing proportion of primary creep strain to total inelastic strain under different thermal profiles. The constant-load creep and stress relaxation data for Sn3.8Ag0.7Cu span a range of strain rates 10(-8) 1/s < strain rate < 10(-4) 1/s, and temperatures 25°C, 75°C and 100°C. Creep and stress relaxation measurements show that transient creep caused faster strain rates during stress relaxation for a given stress compared to the corresponding minimum creep rate from constant-load creep tests. The extent of strain hardening during primary creep was a function of temperature and strain rate. A constitutive creep model was presented for Sn3.8Ag0.7Cu that incorporates both transient and steady-state creep to provide agreement for both creep and stress relaxation data with a single set of eight coefficients. The model utilizes both temperature compensated time and strain rate to normalize minimum strain rate and saturated transient creep strain, thereby establishing equivalence between decreased temperature and increased strain rate. The apparent activation energy of steady-state creep was indicative of both dislocation core and bulk lattice diffusion was the most sensitive model parameter. A saturation threshold was defined that distinguishes whether primary or secondary creep is dominant under either static or variable loading.

This paper provides simulation evidence concerning some statistical properties of two different approaches to technical efficiency estimation for multiple-output production under noisy conditions: The Ray Frontier Approach (RFA) from Löthgren (1997) DEA+ proposed in Gstach (1996). RFA, unlike earlier approaches in the realm of stochastic frontier analysis, is capable of efficiency estimation in the case of multiple outputs as well and lends itself for comparison with DEA+. Several settings with varying sample sizes, noise to signal ratios and mean inefficiencies are investigated. (author's abstract) / Series: Department of Economics Working Paper Series

A novel trajectory and attitude control and navigation analysis tool for powered ascent is developed. The tool is capable of rapid trade-space analysis and is designed to ultimately reduce turnaround time for launch vehicle design, mission planning, and redesign work. It is streamlined to quickly determine trajectory and attitude control dispersions, propellant dispersions, orbit insertion dispersions, and navigation errors and their sensitivities to sensor errors, actuator execution uncertainties, and random disturbances. The tool is developed by applying both Monte Carlo and linear covariance analysis techniques to a closed-loop, launch vehicle guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight GN&C software models of a closed-loop, six-degree-of-freedom (6-DOF), Monte Carlo simulation are formulated and developed. The nominal reference trajectory (NRT) for the proposed lunar ascent trajectory is defined and generated. The Monte Carlo truth models and GN&C algorithms are linearized about the NRT, the linear covariance equations are formulated, and the linear covariance simulation is developed. The performance of the launch vehicle GN&C system is evaluated using both Monte Carlo and linear covariance techniques and their trajectory and attitude control dispersion, propellant dispersion, orbit insertion dispersion, and navigation error results are validated and compared. Statistical results from linear covariance analysis are generally within 10% of Monte Carlo results, and in most cases the differences are less than 5%. This is an excellent result given the many complex nonlinearities that are embedded in the ascent GN&C problem. Moreover, the real value of this tool lies in its speed, where the linear covariance simulation is 1036.62 times faster than the Monte Carlo simulation. Although the application and results presented are for a lunar, single-stage-to-orbit (SSTO), ascent vehicle, the tools, techniques, and mathematical formulations that are discussed are applicable to ascent on Earth or other planets as well as other rocket-powered systems such as sounding rockets and ballistic missiles.

To propose a methodology for the uncertainty estimation in water quality modeling as related to TMDL development, four Monte Carlo (MC) based techniques—single-phase MC, two-phase MC, Generalized Likelihood Uncertainty Estimation (GLUE), and Markov Chain Monte Carlo (MCMC) —were applied to a Hydrological Simulation Program–FORTRAN (HSPF) model developed for the Mossy Creek bacterial TMDL in Virginia. Predictive uncertainty in percent violations of instantaneous fecal coliform concentration criteria for the prediction period under two TMDL pollutant allocation scenarios was estimated. The average percent violations of the applicable water quality criteria were less than 2% for all the evaluated techniques. Single-phase MC reported greater uncertainty in percent violations than the two-phase MC for one of the allocation scenarios. With the two-phase MC, it is computationally expensive to sample the complete parameter space, and with increased simulations, the estimates of single and two-phase MC may be similar. Two-phase MC reported significantly greater effect of knowledge uncertainty than stochastic variability on uncertainty estimates. Single and two-phase MC require manual model calibration as opposed to GLUE and MCMC that provide a framework to obtain posterior or calibrated parameter distributions based on a comparison between observed and simulated data and prior parameter distributions. Uncertainty estimates using GLUE and MCMC were similar when GLUE was applied following the log-transformation of observed and simulated FC concentrations. GLUE provides flexibility in selecting any model goodness of fit criteria for calculating the likelihood function and does not make any assumption about the distribution of residuals, but this flexibility is also a controversial aspect of GLUE. MCMC has a robust formulation that utilizes a statistical likelihood function, and requires normal distribution of model errors. However, MCMC is computationally expensive to apply in a watershed modeling application compared to GLUE. Overall, GLUE is the preferred approach among all the evaluated uncertainty estimation techniques, for the application of watershed modeling as related to bacterial TMDL development. However, the application of GLUE in watershed-scale water quality modeling requires further research to evaluate the effect of different likelihood functions, and different parameter set acceptance/rejection criteria. / Ph. D.

Effective pollution mitigation is the key to successful air quality management. Although states invest millions of dollars to predict future air quality, the regulatory modeling and analysis process to inform pollution control strategy remains uncertain. Traditionally deterministic ‘bright-line’ tests are applied to evaluate the sufficiency of a control strategy to attain an air quality standard. A critical part of regulatory attainment demonstration is the prediction of future pollutant levels using photochemical air quality models. However, because models are uncertain, they yield a false sense of precision that pollutant response to emission controls is perfectly known and may eventually mislead the selection of control policies. These uncertainties in turn affect the health impact assessment of air pollution control strategies. This thesis explores beyond the conventional practice of deterministic attainment demonstration and presents novel approaches to yield probabilistic representations of pollutant response to emission controls by accounting for uncertainties in regional air quality planning. Computationally-efficient methods are developed and validated to characterize uncertainty in the prediction of secondary pollutant (ozone and particulate matter) sensitivities to precursor emissions in the presence of uncertainties in model assumptions and input parameters. We also introduce impact factors that enable identification of model inputs and scenarios that strongly influence pollutant concentrations and sensitivity to precursor emissions. We demonstrate how these probabilistic approaches could be applied to determine the likelihood that any control measure will yield regulatory attainment, or could be extended to evaluate probabilistic health benefits of emission controls, considering uncertainties in both air quality models and epidemiological concentration–response relationships. Finally, ground-level observations for pollutant (ozone) and precursor concentrations (oxides of nitrogen) have been used to adjust probabilistic estimates of pollutant sensitivities based on the performance of simulations in reliably reproducing ambient measurements. Various observational metrics have been explored for better scientific understanding of how sensitivity estimates vary with measurement constraints. Future work could extend these methods to incorporate additional modeling uncertainties and alternate observational metrics, and explore the responsiveness of future air quality to project trends in emissions and climate change.

This thesis deals with the investment project. The subject of the investment project is the construction of a new production hall and the purchase of new manufacturing technologies. The thesis focuses on the characteristics of each part of the feasibility study and detailed analysis of several parts. The thesis also deals with assessing the economic efficiency of the investment by calculating economic indicators. These indicators evaluate the investment plan as suitable or unsuitable for implementation. On the calculation of economic indicators continues probabilistic analysis. The probabilistic analysis is important to determine the level of risk in advance to facilitate investment decisions.

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