# Local Entropy Optimization–Adaptive Demodulation Reassignment Transform for Advanced Analysis of Non-Stationary Mechanical Signals

## TL;DR

A new method called LEOADRT improves the analysis of complex mechanical signals by optimizing time-frequency resolution for better fault diagnosis and monitoring.

## Contribution

The novel LEOADRT method introduces a demodulation term and Rényi entropy optimization for enhanced non-stationary signal analysis.

## Key findings

- LEOADRT outperforms existing methods in processing complex non-stationary signals with closely spaced frequencies.
- The method improves time-frequency resolution using energy redistribution based on maximum local energy criterion.
- It is effective for real-time analysis of multi-component and cross-frequency mechanical signals.

## Abstract

This research proposes a new method for time–frequency analysis, termed the Local Entropy Optimization–Adaptive Demodulation Reassignment Transform (LEOADRT), which is specifically designed to efficiently analyze complex, non-stationary mechanical vibration signals that exhibit multiple instantaneous frequencies or where the instantaneous frequency ridges are in close proximity to each other. The method introduces a demodulation term to account for the signal’s dynamic behavior over time, converting each component into a stationary signal. Based on the local optimal theory of Rényi entropy, the demodulation parameters are precisely determined to optimize the time–frequency analysis. Then, the energy redistribution of the ridges already generated in the time–frequency map is performed using the maximum local energy criterion, significantly improving time–frequency resolution. Experimental results demonstrate that the performance of the LEOADRT algorithm is superior to existing methods such as SBCT, EMCT, VSLCT, and GLCT, especially in processing complex non-stationary signals with non-proportionality and closely spaced frequency intervals. This method provides strong support for mechanical fault diagnosis, condition monitoring, and predictive maintenance, making it particularly suitable for real-time analysis of multi-component and cross-frequency signals.