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

该项目确定结构和基础设施工程（SIE）的指标，并探讨分析和模拟方法，量化这些指标。在这项研究中研究的SIE指标包括：可靠性，鲁棒性，冗余，弹性，风险，可持续性和生命周期成本。鉴于这些指标有不同的语义角度，他们的量化还没有探索使用计算和算法思维，而这项研究这样做。该研究还研究了每个指标的计算限制，并利用精确和近似公式的机会。可计算的度量为SIE系统的设计、构建、维护和恢复提供了信息。此外，本研究还涉及了不同的学生群体，计算算法将成为SIE系统设计的一种机制，探索了SIE应用的度量分类，同时通过数学证明证明了这些度量对计算复杂性层次的隶属关系。证明主要是通过多项式时间内的可约链，特殊的子程序，如预言机，而组合参数揭示了使用不同的策略，无论是精确或近似追求哪些指标。例如，该研究探讨了层次结构底部的度量的递归公式，并寻求额外的证明来确定为什么实际约束（如可靠性的相关性）会将问题的结构分解为指数时间算法。该项目探索对称性，周期性和其他功能，支持概率算法的公差和置信水平是可以接受的大型SIE问题的实例。

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.