Successful dam design endeavor involves generating technical solutions that can meet intended functional objectives and choosing the best one among the alternative technical solutions. The process of choosing the best among the alternative technical solutions depends on evaluation of design conformance with technical specifications and reliability standards (such as capacity, environmental, safety, social, political etc pecifications). The process also involves evaluation on whether an optimal balance is set between safety and economy. The process of evaluating alternative design solutions requires generating a quantitative expression for lifetime performance and safety. An objective and numerical evaluation of lifetime performance and safety of dams is an essential but complex undertaking. Its domain involves much uncertainty (uncertainty in loads, hazards, strength parameters, boundary conditions, models and dam failure consequences) all of which should be characterized. Arguably uncertainty models and risk analysis provide the most complete characterization of dam performance and safety issues. Risk is a combined measure of the probability and severity of an adverse effect (functional and/or structural failure), and is often estimated by the product of the probability of the adverse event occurring and the expected consequences. Thus, risk analysis requires (1) determination of failure probabilities. (2) probabilistic estimation of consequences. Nonetheless, there is no adequately demonstrated, satisfactorily comprehensive and precise method for explicit treatment and integration of all uncertainties in variables of dam design and risk analysis. Therefore, there is a need for evaluating existing uncertainty models for their applicability, to see knowledge and realization gaps, to drive or adopt new approaches and tools and to adequately demonstrate their practicability by using real life case studies. This is required not only for hopefully improving the performance and safety evaluation process accuracy but also for getting better acceptance of the probabilistic approaches by those who took deterministic design based research and engineering practices as their life time career. These problems have motivated the initiation of this research. In this research the following have been accomplished: (1) Identified various ways of analyzing and representing uncertainty in dam design parameters pertinent to three dominant dam failure causes (sliding, overtopping and seepage), and tested a suite of stochastic models capable of capturing design parameters uncertainty to better facilitate evaluation of failure probabilities; (2) Studied three classical stochastic models: Monte Carlo Simulation Method (MCSM), First Order Second Moment (FOSM) and Second Order Second Moment (SOSM), and applied them for modeling dam performance and for evaluating failure probabilities in line with the above mentioned dominant dam failure causes; (3) Presented an exact new for the purpose analytical method of transforming design parameters distributions to a distribution representing dam performance (Analytical Solution for finding Derived Distributions (ASDD) method). Laid out proves of its basic principles, prepared a generic implementation architecture and demonstrated its applicability for the three failure modes using a real life case study data; (4) Presented a multitude of tailor-made reliability equations and solution procedures that will enable the implementations of the above stochastic and analytical methods for failure probability evaluation; (5) Implemented the stochastic and analytical methods using real life data pertinent to the three failure mechanisms from Tendaho Dam, Ethiopia. Compared the performance of the various stochastic and analytical methods with each other and with the classical deterministic design approach; and (6) Provided solution procedures, implementation architectures, and Mathematica 5.2, Crystal Ball 7 and spreadsheet based tools for doing the above mentioned analysis. The results indicate that: (1) The proposed approaches provide a valid set of procedures, internally consistent logic and produce more realistic solutions. Using the approaches engineers could design dams to meet a quantified level of performance (volume of failure) and could set a balance between safety and economy; (2) The research is assumed to bridge the gap between the available probability theories in one hand and the suffering distribution problems in dam safety evaluation on the other; (3) Out of the suite of stochastic approaches studied the ASDD method out perform the classical methods (MCSM, FOSM and SOSM methods) by its theoretical foundation, accuracy and reproducibility. However, when compared with deterministic approach, each of the stochastic approaches provides valid set of procedures, consistent logic and they gave more realistic solution. Nonetheless, it is good practice to compare results from the proposed probabilistic approaches; (4) The different tailor-made reliability equations and solution approaches followed are proved to work for stochastic safety evaluation of dams; and (5) The research drawn from some important conclusions and lessons, in relation to stochastic safety analysis of dams against the three dominant failure mechanisms, are. The end result of the study should provide dam engineers and decision makers with perspectives, methodologies, techniques and tools that help them better understand dam safety related issues and enable them to conduct quantitative safety analysis and thus make intelligent dam design, upgrading and rehabilitation decisions.

This thesis discusses a methodology for probabilistic design optimization of aircraft structures subject to a multidisciplinary set of requirements originating from the desire to minimize structural weight while fulfilling the demands for quality, safety, producibility, and affordability. With this design methodology as the framework, a software is developed, which is capable of performing design optimization of metallic built-up beam structures where the material properties, external load, as well as the structural dimensions are treated as probabilistic random variables. The structural and failure analyses are based on analytical and semi-empirical methods whereas the component reliability analysis is based on advanced first-order second moment method. Metrics-based analytical models are used for the manufacturability analysis of individual parts with the total manufacturing cost estimated using models derived from the manufacturing cost / design guide developed by the Battelle¡¯s Columbus Laboratories. The resulting optimization problem is solved using the method of sequential quadratic programming. A wing spar design optimization problem is used as a demonstrative example including a comparison between non-buckling and buckling web design concepts. A sensitivity analysis is performed and the optimization results are used to highlight the tradeoffs among weight, reliability, and manufacturing cost.

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.

Parameter variations, noise susceptibility, and increasing energy dissipation of CMOS devices have been recognized as major challenges in circuit and micro-architecture design in the nanometer regime. Among these, parameter variations and noise susceptibility are increasingly causing CMOS devices to behave in an "unreliable" or "probabilistic" manner. To address these challenges, a shift in design paradigm, from current day deterministic designs to "statistical" or "probabilistic" designs is deemed inevitable. Motivated by these considerations, I introduce and define probabilistic Boolean logic, whose logical operators are by definition "correct" with a probability 1/2 <= p <= 1. While most of the laws of conventional Boolean logic can be naturally extended to be valid in the probabilistic case, there are a few significant departures. We also show that computations realized using implicitly probabilistic Boolean operators are more energy efficient than their counterparts which use explicit sources of randomness, in the context of probabilistic Boolean circuits as well as probabilistic models with state, Rabin automata. To demonstrate the utility of implicitly probabilistic elements, we study a family of probabilistic architectures: the probabilistic system-on-a-chip PSOC, based on CMOS devices rendered probabilistic due to noise, referred to as probabilistic CMOS or PCMOS devices. These architectures yield significant improvements, both in the energy consumed as well as in the performance in the context of probabilistic or randomized applications with broad utility. Finally, we extend the consideration of probability of correctness to arithmetic operations, through probabilistic arithmetic. We show that in the probabilistic context, substantial savings in energy over correct arithmetic operations may be achieved. This is the theoretical basis of the energy savings reported in the video decoding and radar processing applications that has been demonstrated in prior work.

Several techniques were studied to select and prioritize technologies for a complex system. Based on the findings, a method called Pareto Optimization and Selection of Technologies (POST) was formulated to efficiently explore the combinatorial technology space. A knapsack problem was selected as a benchmark problem to test-run various algorithms and techniques of POST. A Monte Carlo simulation using the surrogate models was used for uncertainty quantification. The concepts of graph theory were used to model and analyze compatibility constraints among technologies. A probabilistic Pareto optimization, based on the concepts of Strength Pareto Evolutionary Algorithm II (SPEA2), was formulated for Pareto optimization in an uncertain objective space. As a result, multiple Pareto hyper-surfaces were obtained in a multi-dimensional objective space; each hyper-surface representing a specific probability level. These Pareto layers enabled the probabilistic comparison of various non-dominated technology combinations. POST was implemented on a technology exploration problem for a 300 passenger commercial aircraft. The problem had 29 identified technologies with uncertainties in their impacts on the system. The distributions for these uncertainties were defined using beta distributions. Surrogate system models in the form of Response Surface Equations (RSE) were used to map the technology impacts on the system responses. Computational complexity of technology graph was evaluated and it was decided to use evolutionary algorithm for probabilistic Pareto optimization. The dimensionality of the objective space was reduced using a dominance structure preserving approach. Probabilistic Pareto optimization was implemented with reduced number of objectives. Most of the technologies were found to be active on the Pareto layers. These layers were exported to a dynamic visualization environment enabled by a statistical analysis and visualization software called JMP. The technology combinations on these Pareto layers are explored using various visualization tools and one combination is selected. The main outcome of this research is a method based on consistent analytical foundation to create a dynamic tradeoff environment in which decision makers can interactively explore and select technology combinations.

Probabilistic finite element analysis was used to determine whether there is a statistically significant relationship between maximum principal strain orientations and orthotropic material stiffness orientations in a primate cranium during mastication. We first sought to validate our cranium finite element model by sampling in-vivo strain and in-vivo muscle activation data during specimen mastication. A comparison of in vivo and finite element predicted (i.e. in silico) strains was performed to establish the realism of the FEM model. To the best of our knowledge, this thesis presents the world’s only complete in-vivo coupled with in-vitro validation data set of a primate cranium FEM. Our results indicate that a validated FEM of a Cebus apella cranium was achieved. Giving collaborating anthropologists, biologists, and engineers the confidence that these models have sufficient accuracy to address the research questions pertaining to cranial structure morphology. Probabilistic finite element analysis design was then utilized to determine the dependence of maximum principal strain orientations on material stiffness orientations in particular craniofacial regions during mastication. It was discovered that the maximum principal strain orientations are more dependent on loading conditions and/or the shape of and location in the cranium rather than the material stiffness orientation of a particular region. It was also uncovered that the material stiffness orientations are not developed in a way that is optimal for feeding biomechanics from the perspective of minimization of total elastic strain energy. Results from this research will provide insights into the co-evolution of bone morphology and material properties in the facial skeleton.

A gas turbine engine design process was developed for the design of a common core engine family. The process considers initial and projected variant engine applications, likely technology maturation, and various sources of uncertainty when making initial core design considerations. A physics based modeling and simulation environment was developed to enforce geometric core commonality between the core defining design engine and a common core variant engine. The environment also allows for upgrade options and technology to be infused into the variant engine design. The relationships established in the model enable commonality to be implicitly enforced when performing simultaneous design space explorations of the common core design and all corresponding variant engine designs. A robust design simulation process was also developed, enabling probabilistic surrogate model representations of the common core engine family design space to be produced. The probabilistic models provide confidence interval performance estimates with a single function call for an inputted set of core and variant design settings and the uncertainty distribution shape parameter settings representative of an uncertainty scenario of interest. The unique form of the probabilistic surrogate models enables large numbers of common core engine family applications to be considered simultaneously, each being simulated under a unique uncertainty scenario. Implications of core design options can be instantaneously predicted for all engine applications considered, allowing for favorable common core design regions to be identified in a highly efficient manner.

Diploma thesis is focused on advanced reliability analysis of structures solved by non--linear finite element analysis. Specifically, semi--probabilistic methods for determination of design value of resistance, sensitivity analysis and surrogate model created by polynomial chaos expansion are described in the diploma thesis. Described methods are applied on prestressed reinforced concrete roof girder.