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

本项目确定结构和基础设施工程(SIE)指标，并探索量化这些指标的分析和模拟方法。本研究研究的SIE指标包括：可靠性、稳健性、冗余度、恢复力、风险、可持续性和生命周期成本。鉴于这些指标具有不同的语义视角，因此本研究并未使用计算和算法思维来探讨它们的量化。这项研究还研究了每个指标的计算极限，并利用机会获得精确和近似的公式。可计算的指标指导SIE系统的设计、构建、维护和恢复的实践。此外，研究还涉及不同的学生群体，计算算法将成为SIE系统设计的一种机制。本文探索了SIE应用的指标分类，并通过数学证明证明了这些指标在计算复杂性层次中的隶属关系。证明主要是通过多项式时间内的可约化链和特殊的子例程(如预言)来实现的，而组合论证则揭示了使用不同的策略来追求哪些度量，无论是精确的还是近似的。例如，这项研究探索了层次结构底部指标的递归公式，并寻求额外的证据来确定为什么实际约束，如可靠性的相关性，将问题的结构分解为指数时间算法。该项目探索了对称性、周期性和其他支持概率算法的特征，这些特征的容差和置信度对于大型SIE问题实例是可接受的。

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.