This research aims to develop an accurate and efficient method for reliability analysis of computationally and probabilistically complex structural engineering problems that cannot be accurately solved with current reliability methods without high-cost simulation approaches. This will be accomplished by formulating a simulation-based approach based on the method of conditional expectation and estimation of the probability density of the simulated results in the critical region of interest. The project will develop an optimal algorithm for probability density construction, a method to estimate error in the calculated reliability, and a new and accurate approach for efficient simulation utilizing variance reduction techniques. The methods developed in the project will be validated on a database of benchmark reliability problems as well as selected complex structural reliability problems representative of engineering practice.
This research is expected to advance structural safety analysis for a variety of complex, high-fidelity engineering problems such as crash, impact, and blast analysis; metal forming; and complex structural system evaluation in various engineering disciplines. The work will provide advanced training to undergraduate and graduate students with their possible recruitment from underrepresented groups through existing university outreach programs. Selected research results will be incorporated in the structural engineering curriculum to expose students to state-of-the-art safety analysis methods.
that cannot be accurately solved with current reliability methods without high-cost simulation approaches. The approach was to enhance a recently developed modified conditional expectation method proposed by the PI for probabilistic analysis by integrating it with state-of-the-art concepts from reliability analysis and design optimization. The resulting method produces a uniquely tailored, optimal representation of probability density in the critical region of a given probabilistic problem for an advancement in accurate and efficient reliability analysis. It was found that the developed method could solve a large variety of benchmark structural reliability problems with reasonable accuracy and with computational costs significantly below that of traditional approaches. The feasibility of the method was further verified by accurately solving several complex, computationally demanding engineering problems with similarly relatively small computational effort. Implementation of the method provides an opportunity to advance structural reliability analysis for complex problems, potentially allowing the accurate solution of some problems that may not be computationally feasible by current methods. These problems exist in a wide variety of fields including civil, mechanical, aerospace, naval, and industrial engineering. Examples of such problems are the reliability analysis of structures exposed to impact or blasts, vehicular crashes, metal forming, and other problems with high computational demand. The efficient, high-fidelity solution of such reliability problems may potentially result in structural designs that are more safe as well as more efficient. Moreover, this work provided advanced training to engineering students who were involved in the research and allowed for the completion of a PhD dissertation. Selected research results have been incorporated in the structural engineering curriculum to expose future students to state-of-the-art safety analysis methods.
