# Robust Incipient Fault Diagnosis of Rolling Element Bearings Under Small-Sample Conditions Using Refined Multiscale Rating Entropy

## TL;DR

This paper introduces a new method for detecting early bearing faults in aero-engines using advanced entropy analysis and optimization techniques, even when data is limited.

## Contribution

The study proposes a refined multiscale entropy method and an optimized learning framework for robust fault diagnosis with minimal samples.

## Key findings

- The RTSMRaE-AOO-ELM framework achieved 99.47% diagnostic accuracy with only five training samples per class.
- The method effectively preserves transient features while suppressing noise in limited data scenarios.
- Experimental results show improved stability and generalization over conventional approaches.

## Abstract

The operational reliability of aero-engines is critically dependent on the health of rolling element bearings, while incipient fault diagnosis remains particularly challenging under small-sample conditions. Although multiscale entropy methods are widely used for complexity analysis, conventional coarse-graining strategies suffer from severe information loss and unstable estimation when data are extremely limited. To address this, the primary objective of this study is to develop a robust diagnostic framework that ensures feature consistency and classification stability even with minimal training samples. Specifically, this paper proposes an integrated approach combining Refined Time-shifted Multiscale Rating Entropy (RTSMRaE) with an Animated Oat Optimization (AOO)-optimized Extreme Learning Machine (ELM). By introducing a refined time-shift operator and a dual-weight fusion mechanism, RTSMRaE effectively preserves transient impulsive features across multiple scales while suppressing stochastic fluctuations. Meanwhile, the AOO algorithm is employed to optimize the input weights and hidden biases of the ELM, alleviating performance instability caused by random initialization and improving generalization capability. Experimental validation on both laboratory-scale and real-world aviation bearing datasets demonstrates that the proposed RTSMRaE-AOO-ELM framework achieves a diagnostic accuracy of 99.47% with a standard deviation of ±0.48% using only five training samples per class. These results indicate that the proposed method offers superior diagnostic robustness and computational efficiency, providing a promising solution for intelligent condition monitoring in data-scarce industrial environments.