# Robust Fractional Low Order Adaptive Linear Chirplet Transform and Its Application to Fault Analysis

## TL;DR

This paper introduces new methods for analyzing mechanical fault vibrations in noisy environments using advanced time-frequency analysis techniques.

## Contribution

The novel contribution is the development of robust fractional low-order adaptive chirplet transforms for noise suppression in fault vibration signals.

## Key findings

- The proposed FLOACT and FLOASCT methods effectively handle mixed noise in time-frequency analysis.
- Improved methods show good performance in estimating fault signals with lower mean square noise ratio.
- Experimental results confirm robustness and adaptability in complex noise environments.

## Abstract

Time-frequency analysis (TFA) technology is an important tool for analyzing non-Gaussian mechanical fault vibration signals. In the complex background of infinite variance process noise and Gaussian colored noise, it is difficult for traditional methods to obtain the highly concentrated time-frequency representation (TFR) of fault vibration signals. Based on the insensitive property of fractional low-order statistics for infinite variance and Gaussian processes, robust fractional lower order adaptive linear chirplet transform (FLOACT) and fractional lower order adaptive scaling chirplet transform (FLOASCT) methods are proposed to suppress the mixed complex noise in this paper. The calculation steps and processes of the algorithms are summarized and deduced in detail. The experimental simulation results show that the improved FLOACT and FLOASCT methods have good effects on multi-component signals with short frequency intervals in the time-frequency domain and even cross-frequency trajectories in the strong impulse background noise environment. Finally, the proposed methods are applied to the feature analysis and extraction of the mechanical outer race fault vibration signals in complex background environments, and the results show that they have good estimation accuracy and effectiveness in lower MSNR, which indicate their robustness and adaptability.