A Generalized Fisher Discriminant Analysis with Adaptive Entropic Regularization for Cross-Model Vibration State...

Area of Science:

• Aerospace Engineering
• Mechanical Engineering
• Vibration Analysis

Background:

• Wind tunnel testing is crucial for aerodynamic analysis and structural integrity.
• Aeroelastic instabilities like flutter present significant risks during testing.
• Current monitoring systems often lack real-time, model-agnostic capabilities.

Purpose of the Study:

• To develop a novel, generalized health indicator (HI) for real-time, model-agnostic vibration monitoring.
• To improve the early detection of dangerous vibration states and aeroelastic instabilities.
• To enhance the cross-model applicability of vibration monitoring systems.

Main Methods:

• A generalized health indicator (HI) based on an improved Fisher Discriminant Analysis (FDA) framework.
• Reformulation of the FDA objective function for stable vs. dangerous state classification.
• Frequency-wise standardization and dual-mode entropic regularization for cross-model generalization and sensitivity.

Main Results:

• The proposed HI effectively distinguishes between stable and dangerous vibration states.
• Frequency-wise standardization ensures cross-model applicability.
• Dual-mode entropic regularization enhances sensitivity to critical resonance frequencies.

Conclusions:

• The novel HI method demonstrates superior performance in early detection of dangerous vibrations.
• The approach offers clear interpretability of critical frequency bands.
• The method shows advantages in trendability, robustness, and cross-model adaptation compared to existing techniques.