# A Generalized Fisher Discriminant Analysis with Adaptive Entropic Regularization for Cross-Model Vibration State Monitoring in Wind Tunnels

## TL;DR

This paper introduces a new method for monitoring vibrations in wind tunnel models to detect dangerous states early and adapt across different models.

## Contribution

The paper proposes a generalized Fisher Discriminant Analysis with adaptive entropic regularization for cross-model vibration monitoring.

## Key findings

- The method successfully detects dangerous vibrations earlier than traditional methods.
- The approach demonstrates robustness and adaptability across different wind tunnel models.
- The entropic regularization improves generalizability and sensitivity to critical frequencies.

## Abstract

The vibration monitoring of scaled models in wind tunnels is critical for aerodynamic testing and structural safety. The abrupt onset of flutter or other aeroelastic instabilities poses a significant risk, necessitating the development of real-time, model-agnostic monitoring systems. This paper proposes a novel, generalized health indicator (HI) based on an improved Fisher Discriminant Analysis (FDA) framework for vibration state classification. The core innovation lies in reformulating the FDA objective function to distinguish between stable and dangerous vibration states, rather than tracking degradation trends. To ensure cross-model applicability, a frequency-wise standardization technique is introduced, normalizing spectral amplitudes based on the statistics of a model’s stable state. Furthermore, a dual-mode entropic regularization term is incorporated into the optimization process. This term balances the dispersion of weights across frequency bands (promoting generalizability and avoiding overfitting to specific frequencies) with the concentration of weights on the most informative resonance frequencies (enhancing the sensitivity to dangerous states). The optimal frequency weights are obtained by solving a regularized generalized eigenvalue problem, and the resulting HI is the weighted sum of the standardized frequency amplitudes. The method is validated using simulated spectral data and flight data from a wind tunnel test, demonstrating a superior performance in the early detection of dangerous vibrations and the clear interpretability of critical frequency bands. Comparisons with traditional sparse measures and machine-learning methods highlight the proposed method’s advantages in trendability, robustness, and unique capability for cross-model adaptation.