  Dynamical system-based linear transfer Perron- Frobenius (P-F) operator
framework is developed to address analysis and design problems in the building
system. In particular, the problems of fast contaminant propagation and optimal
placement of sensors in uncertain operating conditions of indoor building
environment are addressed. The linear nature of transfer P-F operator is
exploited to develop a computationally efficient numerical scheme based on the
finite dimensional approximation of P-F operator for fast propagation of
contaminants. The proposed scheme is an order of magnitude faster than existing
methods that rely on simulation of an advection-diffusion partial differential
equation for contami- nant transport. Furthermore, the system-theoretic notion
of observability gramian is generalized to nonlinear flow fields using the
transfer P-F operator. This developed notion of observability gramian for
nonlinear flow field combined with the finite dimensional approximation of P-F
operator is used to provide a systematic procedure for optimal placement of
sensors under uncertain operating conditions. Simulation results are presented
to demonstrate the applicability of the developed framework on the IEA-annex 2D
benchmark problem.
