Probabilistic Deep Discriminant Analysis for Wind Blade Segmentation

2026-01-20

AI Summary

Traditional linear discriminant analysis struggles to effectively address the nonlinear separability inherent in wind turbine blade image segmentation, often resulting in severe inter-class overlap and low prediction confidence. To overcome this limitation, this work proposes Probabilistic Deep Discriminant Analysis (PDDA), which, for the first time, adapts deep discriminant analysis to image segmentation by directly optimizing the Fisher criterion through a deep network. The approach incorporates signed between-class variance, Sigmoid output constraints, and a multiplication-to-addition strategy to formulate two stable DDA loss functions, further integrated with a probabilistic loss. This method substantially reduces intra-class variance and enhances class separability, significantly improving segmentation accuracy and consistency for wind turbine blades, thereby offering highly reliable visual inspection capabilities for wind energy operation and maintenance.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Multi-instance/Multi-view Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Web data integration and cleaning

Abstract

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks. To ensure stable training and avoid computational instabilities, we incorporate signed between-class variance, bound outputs with a sigmoid function, and convert multiplicative relationships into additive ones. We present two stable DDA loss functions and augment them with a probability loss, resulting in Probabilistic DDA (PDDA). PDDA effectively minimizes class overlap in output distributions, producing highly confident predictions with reduced within-class variance. When applied to wind blade segmentation, PDDA showcases notable advances in performance and consistency, critical for wind energy maintenance. To our knowledge, this is the first application of DDA to image segmentation.

Problem

• Linear Discriminant Analysis
• Non-linearly separable data
• Wind blade segmentation
• Class separability
• Image segmentation

Innovation

• Deep Discriminant Analysis
• Fisher criterion
• Probabilistic DDA
• Image segmentation
• Wind blade