An Integrated Multi-Scale Stochastic Framework for Dynamic Analysis and Control of Transport Phenomena in Building Systems

摘要该项目提出了一种基于动态系统的集成框架，用于分析、检测和控制各种建筑系统应用中的传输过程。 该提案的前提是，交通模型的复杂性是阻碍有效的集成建筑系统解决方案的关键技术障碍。用于评估性能的基于 CFD 的蒙特卡罗模拟效率不高，而且复杂的模型不适合检测、控制或设计。该提案的目标是开发并通过计算演示一个数学框架，该框架能够实现a）动态分析，b）性能基本限制研究，c）传感器架构定义，以及d）建筑系统中复杂运输问题的检测和控制设计。该提案的创新之处在于将传输模型重新塑造为图上的马尔可夫链。马尔可夫链是使用高效的面向集合的方法构建的，以多尺度方式传播不确定性。 这个想法结合了一种多尺度复杂性降低方法来解决构建系统中的各种问题，从而提供了一个集成的建模框架。 该方法还有可能（将被严格探索）利用动力系统和控制理论的最新进展。

AbstractThis project proposes a Dynamical Systems based integrated framework for analysis, detection, and control of transport processes in diverse Building systems applications. The premise of this proposal is that the complexity of transport models is a key technical barrier that prevents effective integrated building system solutions. CFD-based Monte-Carlo simulations for assessing performance is not efficient and complex models are ill-suited for detection, control or design. The objective of the proposal is to develop and demonstrate computationally a mathematical framework that enables a) dynamic analysis, b) study of fundamental limitations in performance, c) sensor architecture definition, and d) detection and control design for complex transport problems in building systems. The innovation of this proposal lies in the re-casting of the transport models as Markov chains on graphs. Markov chains are constructed using efficient set-oriented methods to propagate uncertainty in a multi-scale fashion. This idea incorporates a multi-scale complexity reduction approach to diverse problems in building systems and hence provides for an integrated modeling framework. The approach further has the potential (that will be rigorously explored) to exploit recent advances in both Dynamical Systems and Control Theory.