  Energy efficiency is a big concern in industrial sectors. Finding the root
cause of anomaly state of energy efficiency can help to improve energy
efficiency of industrial systems and therefore save energy cost. In this
research, we propose to use transfer entropy (TE) for root cause analysis on
energy efficiency of industrial systems. A method, called TE flow, is proposed
in that a TE flow from physical measurements of each subsystem to the energy
efficiency indicator along timeline is considered as causal strength for
diagnosing root cause of anomaly states of energy efficiency of a system. The
copula entropy-based nonparametric TE estimator is used in the proposed method.
We conducted experiments on real data collected from a compressing air system
to verify the proposed method. Experimental results show that the TE flow
method successfully identified the root cause of the energy (in)efficiency of
the system.
