Transfer Operator Theoretic Framework for Monitoring Building Indoor Environment in Uncertain Operating Conditions

TL;DR

This paper introduces a transfer operator framework for efficiently analyzing and monitoring indoor building environments, enabling fast contaminant propagation prediction and optimal sensor placement under uncertain conditions.

Contribution

It develops a transfer Perron-Frobenius operator approach for rapid contaminant propagation analysis and sensor placement in uncertain indoor environments, improving computational efficiency.

Findings

The proposed scheme is an order of magnitude faster than existing PDE-based methods.

The framework successfully demonstrates contaminant propagation prediction.

Optimal sensor placement is achieved under uncertain conditions.

Abstract

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.