Collaborative Research: Novel Fractional Order Ground Motion Intensity Measures for High Confidence Risk Assessment of Distributed Infrastructures

地震风险评估框架支持在规划防灾和减灾战略时作出风险知情的决策。这些框架依赖于强度测量（IMs）来表示地震事件的强度，并预测关键基础设施组件的行为及其对网络性能和社会经济系统的级联效应。然而，目前采用基于地震动时程的整数阶导数或积分的危害强度度量方法并不理想地预测基础设施的性能，并且可能在区域风险分析的最终结果中引起很大的不确定性。为了消除离散整数阶微分运算对地震强度表征的限制，本研究将基于分数阶微积分的概念，使用新的空间相关地震强度测度类别“á-order地震强度”进行区域基础设施风险评估。该方法和工具通过显著减少不确定性，为结构和基础设施部件的地震反应提供更准确的概率预测，从而增加了对复杂系统地震可靠性和风险评估的信心。这一成就将对负责管理大型分布式基础设施系统风险的业主，以及从相关的风险缓解和响应策略决策中受益的广大公众产生广泛影响。该项目将使用新的分数阶地面运动响应的推导来表征地震强度，包括识别计算效率高的算法来进行分数阶操作。将确定IMs的最佳需求模型形式和á-order，以实现跨区域投资组合预期的各种复杂基础设施组成部分的概率响应预测。该项目还将为分数阶imes开发相关的地震动预测方程（GMPEs），并量化分布式基础设施系统风险评估（例如网络性能、经济损失）中减少的不确定性。这项研究提供的进步将提供更可靠的分析方法，用于整个地区地震的概率表征，有效地模拟对基础设施的物理需求，并提高对由此产生的风险估计的信心。总体不确定性的降低可以促进风险知情的决策，旨在减少地震带的人员伤亡、经济损失和基础设施功能损失。

Seismic risk assessment frameworks support risk-informed decision making in planning strategies for disaster prevention and mitigation. Such frameworks rely on intensity measures (IMs) to represent the strength of earthquake events, and to predict the behavior of key infrastructure components and their cascading effects on network performance and socio-economic systems. However, the current practice of adopting hazard intensity measures based on integer order derivatives or integrals of the ground motion time history is not ideal to predict infrastructure performance, and may induce significant uncertainties in the final outcome of regional risk analyses. In order to release the limitation of discrete integer order differential operations for IM characterization, this research will use new classes of spatially correlated earthquake intensity measures for regional risk assessment of infrastructures termed "á-order IMs" based on concepts from fractional order calculus. The methodology and tools provide more accurate probabilistic predictions of the seismic response of structures and infrastructure components by significantly reducing uncertainties, thus increasing the confidence in seismic reliability and risk assessment of complex systems. This achievement will offer broad impacts to owners charged with managing risks to large distributed infrastructure systems, and the public at large who benefit from associated risk-informed decisions on mitigation and response strategies.The project will use derivation of novel fractional order ground motion responses to characterize earthquake intensity, including identification of computationally efficient algorithms to conduct the fractional order operations. The optimal demand model form and á-order for the IMs will be identified to enable probabilistic response prediction of a wide range of complex infrastructure constituents anticipated across a regional portfolio. The project will also develop correlated ground motion prediction equations (GMPEs) for the fractional order IMs and quantify the resulting reduced uncertainty in risk estimates (e.g. network performance, economic losses) for distributed infrastructure systems. The advancements offered by this research will afford more robust analytical methods for probabilistic characterization of earthquakes across a region, efficient modeling of the physical demand imparted on infrastructures, and increased confidence in resulting risk estimates. The overall uncertainty reduction can advance risk-informed decision making targeted at reducing human casualties, economic losses, and loss of function of infrastructure in seismic zones.