USING STATISTICAL METHODS TO INVESTIGATE THE MAPPING FROM INITIAL VALUES TO THE MULTIPLE STEADY STATES IN COMPLEX BUILDING SIMULATION PROBLEMS
Jinchao Yuan, Leon R. Glicksman
One of the challenges in some building simulations, especially with coupled airflow and thermal phenomena, is predicting the possible occurrence of multiple steady states under the same boundary conditions. Such behavior is introduced by the nonlinearity in the governing dynam- ics, and the initial values typically have some mapping rules to different final steady states. In some simple sys- tems with one or two state variables, such rules may be analytically singled out by applying a dynamical system analysis. However, in complex multivariate systems, such mapping rules are very difficult to be determined analyti- cally. In this study, we used a statistical analysis method to investigate the relations between the initial state vari- ables that determine the mapping from the initial values to the steady states. The method was applied the simulation data of a natural ventilated multi-level building case that can exhibit three different steady states. Statistical sum- maries of both the single-zone initial value characteristics (mean and distribution), and the inter-zonal correlations between state variables were examined. Combined with existing knowledge about the case, the results revealed the formation mechanism of each possible steady state, which is related to different levels of buoyancy/wind force fine- tuning based on single zone temperatures and inter-zonal temperature correlations. The findings promoted the un- derstanding of the governing physics of a relative complex natural ventilation system and provided potential meth- ods to analyze the solution multiplicity related problems in such a system.
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