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State-space methods for calculating concentration dynamics in multizone buildings

机译：计算多区域建筑物集中动态的状态空间方法

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This work explores analytic solutions to contaminant transport in multizone systems as a means of solving concentration dynamics more rapidly and providing insight into system behaviour. A general formulation is developed that is consistent with state-space theory. This is used to provide general and specific solutions for the concentration time series. In particular, an analytical expression is presented for the case of constant system parameters and constant input conditions using the eigenvalues and eigenvectors for the case of a diagonalisable state matrix for the multizone system. A method for using this expression to solve concentrations over a series of varying building and input states is developed, with potential for use as a rapid means of calculating concentrations at any time. In principle, this method could be used as a complementary method for solving concentration dynamics within multizone software. Analytical expressions for cumulative exposure for the same case are also presented. The characteristic behaviour of the solutions and their dependence on the eigenvalues and eigenvectors of the state matrix are explored for the steady state case and the decay solution. In particular, the behaviour in the late decay phase is shown to be characterised by a single decay rate, given by the smallest magnitude eigenvalue, and a fixed concentration ratio, given by the associated eigenvector. The independence of the concentration ratio in this phase to the initial conditions is also demonstrated. Two example cases are used to illustrate these and additional features.
机译：这项工作探索了多区域系统中污染物迁移的分析解决方案，以更快地解决浓度动态变化并提供对系统行为的洞察力。提出了与状态空间理论一致的一般表述。这用于为浓度时间序列提供一般和特定的解决方案。特别地，对于多区域系统的对角线状态矩阵的情况，使用特征值和特征向量给出了恒定系统参数和恒定输入条件下的解析表达式。开发了一种使用该表达式来求解一系列变化的构建状态和输入状态下的浓度的方法，并有望在任何时间用作计算浓度的快速手段。原则上，该方法可用作解决多区域软件内浓度动态的补充方法。还提供了同一情况下累积暴露量的分析表达式。对于稳态情况和衰减解，研究了解的特征行为及其对状态矩阵特征值和特征向量的依赖。特别地，显示出衰变后期的行为的特征在于，单个衰变率（由最小的特征值给出）和固定的浓度比（由相关的特征向量给出）。还证明了这一阶段浓度比与初始条件的独立性。使用两个示例案例来说明这些功能和其他功能。

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