A Method for the Combination of Stochastic Time Varying Load Effects

The problem of evaluating the probability that a structure becomes unsafe under a combination of loads, over a given time period, is addressed. The loads and load effects are modeled as either pulse (static problem) processes with random occurrence time, intensity and a specified shape or intermittent continuous (dynamic problem) processes which are zero mean Gaussian processes superimposed 'on a pulse process. The load coincidence method is extended to problems with both nonlinear limit states and dynamic responses, including the case of correlated dynamic responses. The technique of linearization of a nonlinear limit state commonly used in a time-invariant problem is investigated for timevarying combination problems, with emphasis on selecting the linearization point. Results are compared with other methods, namely the method based on upcrossing rate, simpler combination rules such as Square Root of Sum of Squares and Turkstra's rule. Correlated effects among dynamic loads are examined to see how results differ from correlated static loads and to demonstrate which types of load dependencies are most important, i.e., affect' the exceedance probabilities the most. Application of the load coincidence method to code development is briefly discussed.National Science Foundation Grants CME 79-18053 and CEE 82-0759

Probabilistic engineering analysis and design under time-dependent uncertainty

Time-dependent uncertainties, such as time-variant stochastic loadings and random deterioration of material properties, are inherent in engineering applications. Not considering these uncertainties in the design process may result in catastrophic failures after the designed products are put into operation. Although significant progress has been made in probabilistic engineering design, quantifying and mitigating the effects of time-dependent uncertainty is still challenging. This dissertation aims to help build high reliability into products under time-dependent uncertainty by addressing two research issues. The first one is to efficiently and accurately predict the time-dependent reliability while the second one is to effectively design the time-dependent reliability into the product. For the first research issue, new time-dependent reliability analysis methodologies are developed, including the joint upcrossing rate method, the surrogate model method, the global efficient optimization, and the random field approach. For the second research issue, a time-dependent sequential optimization and reliability analysis method is proposed. The developed approaches are applied to the reliability analysis of designing a hydrokinetic turbine blade subjected to stochastic river flow loading. Extension of the proposed methods to the reliability analysis with mixture of random and interval variables is also a contribution of this dissertation. The engineering examples tested in in this work demonstrate that the proposed time-dependent reliability methods can improve the efficiency and accuracy more than 100% and that high reliability can be successfully built into products with the proposed method. The research results can benefit a wide range of areas, such as life cycle cost optimization and decision making --Abstract, page iv

Time- and space-dependent uncertainty analysis and its application in lunar plasma environment modeling

”During an engineering system design, engineers usually encounter uncertainties that ubiquitously exist, such as material properties, dimensions of components, and random loads. Some of these parameters do not change with time or space and hence are time- and space-independent. However, in many engineering applications, the more general time- and space-dependent uncertainty is frequently encountered. Consequently, the system exhibits random time- and space-dependent behaviors, which may result in a higher probability of failure, lower average lifetime, and/or worse robustness. Therefore, it is critical to quantify uncertainty and predict how the system behaves under time- and space- dependent uncertainty. The objective of this study is to develop accurate and efficient methods for uncertainty analysis. This study contains five works. In the first work, an accurate method based on the series expansion, Gauss-Hermite quadrature, and saddle point approximation is developed to calculate high-dimensional normal probabilities. Then the method is applied to estimate time-dependent reliability. In the second work, we develop an adaptive Kriging method to estimate product average lifetime. In the third work, a time- and space-dependent reliability analysis method based on the first-order and second-order methods is proposed. In the fourth work, we extend the existing robustness analysis to time- and space-dependent problems and develop an adaptive Kriging method to evaluate the time- and space-dependent robustness. In the fifth work, we develop an adaptive Kriging method to efficiently estimate the lower and upper bounds of the electric potentials of the photoelectron sheaths near the lunar surface”--Abstract, page iv

Assortative mating and differential male mating success in an ash hybrid zone population

BACKGROUND: The structure and evolution of hybrid zones depend mainly on the relative importance of dispersal and local adaptation, and on the strength of assortative mating. Here, we study the influence of dispersal, temporal isolation, variability in phenotypic traits and parasite attacks on the male mating success of two parental species and hybrids by real-time pollen flow analysis. We focus on a hybrid zone population between the two closely related ash species Fraxinus excelsior L. (common ash) and F. angustifolia Vahl (narrow-leaved ash), which is composed of individuals of the two species and several hybrid types. This population is structured by flowering time: the F. excelsior individuals flower later than the F. angustifolia individuals, and the hybrid types flower in-between. Hybrids are scattered throughout the population, suggesting favorable conditions for their local adaptation. We estimate jointly the best-fitting dispersal kernel, the differences in male fecundity due to variation in phenotypic traits and level of parasite attack, and the strength of assortative mating due to differences in flowering phenology. In addition, we assess the effect of accounting for genotyping error on these estimations. RESULTS: We detected a very high pollen immigration rate and a fat-tailed dispersal kernel, counter-balanced by slight phenological assortative mating and short-distance pollen dispersal. Early intermediate flowering hybrids, which had the highest male mating success, showed optimal sex allocation and increased selfing rates. We detected asymmetry of gene flow, with early flowering trees participating more as pollen donors than late flowering trees. CONCLUSION: This study provides striking evidence that long-distance gene flow alone is not sufficient to counter-act the effects of assortative mating and selfing. Phenological assortative mating and short-distance dispersal can create temporal and spatial structuring that appears to maintain this hybrid population. The asymmetry of gene flow, with higher fertility and increased selfing, can potentially confer a selective advantage to early flowering hybrids in the zone. In the event of climate change, hybridization may provide a means for F. angustifolia to further extend its range at the expense of F. excelsior

Probabilistic models for wind loads and reliability analysis

Probabilistic models and surrogate solution are developed to characterize wind loads acting on the structures and assess the corresponding structural responses of linear systems, respectively. These developments can be regarded as essential building blocks in the prediction of structural reliability subject to extreme wind. In this dissertation, we first review the commonly-used probabilistic models in literature and benchmark these models on a test example to illustrate their properties and examine their advantages and disadvantages. It is shown that the approximations based on these existing models on the extreme estimates exhibit large discrepancies. A new probabilistic model is then proposed to overcome this limitation. The model utilized Markov process whose finite dimensional distribution is characterized in terms of copulas. Finally, an efficient and accurate surrogate model is presented as an alternative to the traditional Monte Carlo method to evaluate the structural responses. The responses are approximated by translation processes whose second-moment properties and marginal distribution are obtained from linear random vibration theory and moment equations. The statements in this dissertation are supported by theoretical arguments and numerical examples