Paper Conference

Proceedings of SimBuild Conference 2010: 4th conference of IBPSA-USA


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

Abstract: 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 dynamics , and the initial values typically have some mapping rules to different final steady states. In some simple systems 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 analytically. In this study, we used a statistical analysis method to investigate the relations between the initial state variables 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 summaries 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 understanding of the governing physics of a relative complex natural ventilation system and provided potential methods to analyze the solution multiplicity related problems in such a system.
Pages: 427 - 433