Collaborative Research: Unraveling the Limits of Computation in Structural and Infrastructure Engineering

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This project identifies structural and infrastructure engineering (SIE) metrics and explores analytical and simulation methods that quantify these metrics. SIE metrics studied in this research include: reliability, robustness, redundancy, resilience, risk, sustainability, and life-cycle cost. Given that these metrics have different semantic perspectives their quantification has not been explored using computational and algorithmic thinking while this research does so. The research also studies the computational limits for each metric and takes advantage of the opportunities for exact and approximate formulations. Computable metrics inform the practice of designing, building, maintenance, and restoration of SIE systems. In addition, the research involves a diverse pool of students for which computational algorithms will be a mechanism for the design of SIE systems.A taxonomy of metrics for SIE applications is explored, while demonstrating via mathematical proofs the membership of these metrics to a computational complexity hierarchy. Proofs are mainly achieved via reducible chains in polynomial time, special subroutines such as oracles, while combinatorial arguments reveal which metrics to pursue using diverse strategies, either exactly or approximately. For instance, the research explores recursive formulations for metrics at the bottom of the hierarchy, and additional proofs are pursued to determine why practical constraints, such as correlations in reliability, break the structure of the problem into exponential time algorithms. The project explores symmetries, periodicities, and other features that support probabilistic algorithms with tolerances and confidence levels that are acceptable for large SIE problem instances.