# Fault Diagnosis Method Based on Scaling Law for On-line Refrigerant Leak Detection

## TL;DR

This paper introduces a physics-informed scaling law for refrigerant leak detection in air-conditioning systems, enabling model transferability across different configurations and improving early fault detection accuracy.

## Contribution

It proposes a novel scaling law based on physical modeling that allows fault detection models to be applied across various system configurations, addressing generalization challenges.

## Key findings

- Scaling exponents are statistically equivalent across different systems.
- The method accurately estimates leak severity from real-world data.
- Early leak detection is feasible with the proposed scaling law.

## Abstract

Early fault detection using instrumented sensor data is one of the promising application areas of machine learning in industrial facilities. However, it is difficult to improve the generalization performance of the trained fault-detection model because of the complex system configuration in the target diagnostic system and insufficient fault data. It is not trivial to apply the trained model to other systems. Here we propose a fault diagnosis method for refrigerant leak detection considering the physical modeling and control mechanism of an air-conditioning system. We derive a useful scaling law related to refrigerant leak. If the control mechanism is the same, the model can be applied to other air-conditioning systems irrespective of the system configuration. Small-scale off-line fault test data obtained in a laboratory are applied to estimate the scaling exponent. We evaluate the proposed scaling law by using real-world data. Based on a statistical hypothesis test of the interaction between two groups, we show that the scaling exponents of different air-conditioning systems are equivalent. In addition, we estimated the time series of the degree of leakage of real process data based on the scaling law and confirmed that the proposed method is promising for early leak detection through comparison with assessment by experts.