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Building fragility describes the likelihood of damage to a building due to random ground motions. Conventional methods for computing building fragilities are either based on statistical extrapolation of detailed analyses on one or two specific buildings or make use of Monte Carlo simulation with these models. However, the Monte Carlo technique usually requires a relatively large number of simulations in order to obtain a sufficiently reliable estimate of the fragilities, and it quickly becomes impractical to simulate the required thousands of dynamic time-history structural analyses for physics-based analytical models. An alternative approach for carrying out the structural simulation is explored in this work. The use of Response Surface Methodology in connection with the Monte Carlo simulations simplifies the process of fragility computation. More specifically, a response surface is sought to predict the structural response calculated from complex dynamic analyses. Computational cost required in a Monte Carlo simulation will be significantly reduced since the simulation is performed on a polynomial response surface function, rather than a complex dynamic model. The methodology is applied to the fragility computation of an unreinforced masonry (URM) building located in the New Madrid Seismic Zone. Different rehabilitation schemes for this structure are proposed and evaluated through fragility curves. Response surface equations for predicting peak drift are generated and used in the Monte Carlo simulation. Resulting fragility curves show that the URM building is less likely to be damaged from future earthquakes when rehabilitation is properly incorporated. The thesis concludes with a discussion of an extension of the methodology to the problem of computing fragilities for a collection of buildings of interest. Previous approaches have considered uncertainties in material properties, but this research incorporates building parameters such as geometry, stiffness, and strength variabilities as well as nonstructural parameters (age, design code) over an aggregation of buildings in the response surface models. Simulation on the response surface yields the likelihood of damage to a group of buildings under various earthquake intensity levels. This aspect is of interest to governmental agencies or building owners who are responsible for planning proper mitigation measures for collections of buildings.

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In this work minimally supported D-optimal designs for response surface models with spatially correlated errors are studied. The spatially correlated errors describe the correlation between two measurements depending on their distance d through the covariance function C(d)=exp(-rd). In one dimensional design space, the minimally supported D-optimal designs for polynomial models with spatially correlated errors include two end points and are symmetric to the center of the design region. Exact solutions for simple linear and quadratic regression models are presented. For models with third or higher order, numerical solutions are given. While in two dimensional design space, the minimally supported D-optimal designs are invariant under translation¡Brotation and reflection. Numerical results show that a regular triangle on the experimental region of a circle is a minimally supported D-optimal design for the first-order response surface model.

To be competitive in the market, it is very important to design cost effective and reliable products. For this purpose, it is necessary to consider reliability as an integral part of the design procedure. Therefore, reliability which is a design parameter that affects cost and safety of a system should be taken into consideration in early phases since it is very difficult to change design at the later phases. Reliability of a rocket motor can be evaluated by reliability testing but these tests are very expensive and difficult since the tests are destructive and test sample size is determined by the binomial law. Because of the difficulties in reliability testing, in early design phases reliability can be evaluated by using reliability prediction results. This thesis report includes application of probabilistic approach for a solid rocket motor design to evaluate its reliability in preliminary design phase. In this study, it is aimed to assess the solid rocket motor ballistic performance reliability and casing structural reliability, determine important parameters affective on the solid rocket motor reliability and find a new design point to improve the reliability. Variations in dimensions and material properties are considered as the sources of failures and the limit states for acceleration, total impulse and maximum stress in the casing are approximated with response surface method by considering these variations. With the response surface functions, Monte Carlo simulation is used to assess failure probability and distributions of the rocket motor performance. Besides the assessment of the reliability, capability of the response surface functions to estimate the rocket motor performance and effects of the input parameters on the rocket motor performance and performance variation are also examined. By considering the effect of the input parameters, a new design point is proposed to decrease the total probability of failure.

In this work, an active flow control method is studied numerically by using a synthetic jet over a NACA 0015 airfoil. Unsteady, turbulent flows over the NACA 0015 airfoil are computed using a Navier-Stokes solver. The Spalart-Allmaras turbulence model is employed in all computations. Unsteady flow solutions are computed in parallel using Parallel Virtual Machine library routines in a computer cluster. The synthetic jet is implemented to the flow solver as a boundary condition. Response Surface Methodology is employed for the optimization of synthetic jet parameters at various angles of attack. The synthetic jet parameters / the jet velocity, the jet location, the jet angle and the jet frequency are optimized to maximize the lift to drag ratio. The optimization study is performed for a constant value of jet power coefficient. The jet slot size is used as a dependent parameter in the optimization studies. The optimization study has shown that the jet velocity and the jet location are the dominant synthetic jet parameters. The optimum synthetic jet angle is observed to be increasing as the angle of attack increases. The optimum jet location is observed to be moving through the leading edge as angle of attack increases for the separated flows. It is observed that the application of the synthetic jet delays the flow separation on the suction side of the airfoil and increases the lift to drag ratio significantly especially at post stall angles of attack. The application of the synthetic jet is observed to be less effective for attached flows.

Active flow control by a jet over a 12.5% thick elliptic profile is investigated numerically. Unsteady flowfields are calculated with a Navier Stokes solver. The numerical method is first validated without the jet and with the presence of steady-blowing and pulsating jets. Three jet types, namely steady, pulsating and synthetic jets, are next compared with each other and it is shown that the most drag reduction is achieved by a synthetic jet and the most lift enhancement is achieved by a steady jet. The influences of the jet location, the jet velocity, the jet frequency, the jet slot length and the jet angle on the flowfield is parametrically studied. It is shown that the jet location and the jet velocity are the most effective parameters. The jet parameters are optimized to minimize the drag coefficient while keeping the jet power constant. The drag is reduced by 32.5% for the angle of attack 0 and by 24% for the angle of attack 4.

The main objective of this study was to optimize the roasting conditions of hazelnuts in microwave-infrared and microwave-convective heating combination ovens by using response surface methodology. It was also aimed to construct regression models for the prediction of quality parameters of hazelnuts as a function of processing conditions. The independent variables were microwave power (10, 30, 50, 70 and 90%), upper-lower infrared power (10, 30, 50, 70 and 90%) and roasting time (2, 3, 4, 5 and 6 min) for microwave-infrared combination roasting. Microwave power (70, 140 and 210W), air temperature (90, 150 and 210&deg / C) and roasting time (5, 15 and 25 min) were the independent variables of microwave-convective heating combination oven. As control, hazelnuts roasted in conventional oven at 150&deg / C for 20 min were used. The quality parameters were L* value, a* value, fracture force and moisture content of the hazelnuts for both microwave assisted ovens. The optimum roasting conditions of microwave-infrared combination oven were determined as 2.5 min of roasting time at 613.8W microwave power, 1800W upper infrared power, and 300W lower infrared power. Hazelnuts roasted at the optimum condition had comparable quality with the conventionally roasted ones. When micro- wave infrared combination oven was used, conventional roasting time of hazelnuts was reduced by 87.5%. Optimum roasting conditions of microwave-convective heating combination oven were 140 W microwave power, 150&deg / C air temperature and 20 min roasting time. High regression coefficients were calculated between the experimental data and predicted values showing that RSM is capable in predicting quality parameters of hazelnuts during microwave assisted roasting.

There are many optimization problems motivated by engineering applications, whose constraints and/or cost functions are computationally expensive to evaluate. What is more derivative information is usually not available or available at a considerable cost. For that reason, classical optimization methods, based on derivatives, are not applicable. This study presents a framework based on available methods in literature to overcome this important problem. First, a penalized model is constructed where the violation of the constraints are added to the cost function. The model is optimized with help of stochastic approximation algorithms until a point satisfying the constraints is obtained. Then, a sample point set satisfying the constraints is obtained by taking advantage of direct search algorithms based sampling strategies. In this context, two search direction estimation methods, convex hull based and estimated radius of curvature of the sample point set based methods can be applicable. Point set is used to create a barrier which imposes a large cost for points near to the boundary. The aim is to obtain convergence to local optima using the most promising direction with help of direct search methods. As regards to the evaluation of the cost function there are two directions to follow: a-) Gradient-based methods, b-) Non-gradient methods. In gradient-based methods, the gradient is approximated using the so-called stochastic approximation algorithms. In the latter case, direct search algorithms based sampling strategy is realized. This study is concluded by using all these ideas in the solution of complicated test problems where the cost and the constraint functions are costly to evaluate.

Modern engineering design tends to use computer simulations such as Finite Element Analysis (FEA) to replace physical experiments when evaluating a quality response, e.g., the stress level in a phone packaging process. The use of computer models has certain advantages over running physical experiments, such as being cost effective, easy to try out different design alternatives, and having greater impact on product design. However, due to the complexity of FEA codes, it could be computationally expensive to calculate the quality response function over a large number of combinations of design and environmental factors. Traditional experimental design and response surface methodology, which were developed for physical experiments with the presence of random errors, are not very effective in dealing with deterministic FEA simulation outputs. In this thesis, we will utilize a spatial statistical method (i.e., Kriging model) for analyzing deterministic computer simulation-based experiments. Subsequently, we will devise a sequential strategy, which allows us to explore the whole response surface in an efficient way. The overall number of computer experiments will be remarkably reduced compared with the traditional response surface methodology. The proposed methodology is illustrated using an electronic packaging example.