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Root Cause Analysis on Energy Efficiency with Transfer Entropy Flow

Jian Ma

TL;DR

This paper tackles root-cause analysis of energy-efficiency anomalies in industrial systems by leveraging Transfer Entropy (TE) within a Copula Entropy (CE) based nonparametric framework. It introduces Transfer Entropy Flow (TE flow), a time-windowed approach that computes $TE_{x\rightarrow y}$ from subsystem signals to a system-wide energy-efficiency indicator and uses the maximum TE per window as the causal strength to diagnose root causes. The CE-based TE estimator enables nonparametric, model-free causality estimation suitable for non-stationary industrial data and is applied to a compressing air system (CAS) with six compressors and six dryers. Results from two real-world data sets demonstrate that the TE flow method identifies the subsystem drivers of energy efficiency and inefficiency over time, offering a practical tool for energy optimization in manufacturing. The work highlights the potential of TE flow to provide actionable, time-resolved root-cause insights in complex industrial processes, with future work extending to more systems and deriving interpretable energy-management rules.

Abstract

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.

Root Cause Analysis on Energy Efficiency with Transfer Entropy Flow

TL;DR

This paper tackles root-cause analysis of energy-efficiency anomalies in industrial systems by leveraging Transfer Entropy (TE) within a Copula Entropy (CE) based nonparametric framework. It introduces Transfer Entropy Flow (TE flow), a time-windowed approach that computes from subsystem signals to a system-wide energy-efficiency indicator and uses the maximum TE per window as the causal strength to diagnose root causes. The CE-based TE estimator enables nonparametric, model-free causality estimation suitable for non-stationary industrial data and is applied to a compressing air system (CAS) with six compressors and six dryers. Results from two real-world data sets demonstrate that the TE flow method identifies the subsystem drivers of energy efficiency and inefficiency over time, offering a practical tool for energy optimization in manufacturing. The work highlights the potential of TE flow to provide actionable, time-resolved root-cause insights in complex industrial processes, with future work extending to more systems and deriving interpretable energy-management rules.

Abstract

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.
Paper Structure (15 sections, 2 theorems, 6 equations, 2 figures)

This paper contains 15 sections, 2 theorems, 6 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Theory of Copula Entropy
  5. Estimating Copula Entropy
  6. Estimating Transfer Entropy via Copula Entropy
  7. Transfer Entropy Flow
  8. Experiments and Results
  9. The system
  10. Data
  11. Experiments
  12. Results
  13. Case 1
  14. Case 2
  15. Conclusions

Key Result

Theorem 1

MI of random variables is equivalent to negative CE:

Figures (2)

  • Figure 1: Results of Case 1.
  • Figure 2: Results of Case 2.

Theorems & Definitions (3)

  • Definition 1: Copula Entropy
  • Theorem 1
  • Corollary 1