Data-Driven Quantitative Evaluation of Fault Diagnosability: Integrating Distance and Direction Similarity Metrics

This paper presents a novel data-driven approach to fault diagnosability analysis for linear discrete-time systems. Current methods rely heavily on single evaluation functions based on distance similarity, which may not fully utilize directional information in different sets of data. To address this limitation, the paper proposes a comprehensive set of quantitative evaluation indices that consider both distance and direction similarity. This approach introduces data-driven residuals and reformulates the fault diagnosability evaluation as an assessment of the differences between the residuals in fault-free and faulty cases. Specifically, the paper presents detectability measures that provide the relative size of the residual evaluation function caused by faults and noise. Additionally, a set of isolability evaluation indices is proposed by combining distance and direction similarity between the residuals in different faulty cases. These indices can potentially serve as a reference for optimizing system configuration and designing fault diagnosis systems. To verify the effectiveness of the proposed method, we analyze the diagnosability of gas regulators using data collected from an experimental platform. The proposed detectability indices are 0.560, 0.780, and 1.067, while the integrated isolability measures are $4.5\times 10^{-7}$ , 0.0046, and 0.0044, providing more detailed and precise information than existing methods.