Fault Diagnosis of Complex Processes Using Sparse Kernel Local Fisher Discriminant Analysis

Area of Science:

• Engineering
• Data Science
• Machine Learning

Background:

• Fisher Discriminant Analysis (FDA) is widely used for supervised dimensionality reduction and fault diagnosis.
• Conventional FDA struggles with data multimodality and lacks interpretability by not prioritizing key faulty variables.
• These limitations reduce classification accuracy and practical feasibility in complex industrial processes.

Purpose of the Study:

• To develop an improved Fisher Discriminant Analysis model that addresses the limitations of conventional FDA.
• To enhance fault diagnosis accuracy and model interpretability in complex systems.
• To introduce a robust method capable of handling data multimodality and identifying critical fault indicators.

Main Methods:

• Proposed a Sparse Local Fisher Discriminant Analysis (SLFDA) model incorporating local weighting factors to preserve within-class multimodality.
• Utilized the elastic net algorithm for automatic identification of responsible faulty variables.
• Employed the feasible gradient direction method for optimization and extended the model to a nonlinear variant using the kernel trick (sparse kernel local FDA).

Main Results:

• The SLFDA model effectively preserves data multimodality and enhances fault diagnosis performance.
• Automatic identification of faulty variables significantly improves model interpretability.
• The nonlinear variant demonstrates increased resistance to strong nonlinearity, outperforming existing methods.

Conclusions:

• The novel SLFDA strategy significantly enhances fault diagnosis accuracy and model interpretability compared to conventional FDA.
• The method's ability to handle multimodality and identify key variables makes it a reliable tool for complex industrial processes.
• The sparse kernel local FDA offers a robust solution for nonlinear systems, validating the strategy's effectiveness on benchmark and real-world data.