Application of PCA, DPCA, KPCA, and KSPCA in Fault Identification

In industrial applications, fault identification, diagnosis, and classification play critical roles in maintaining system reliability. Tools such as PCA (Principal Component Analysis), DPCA (Dynamic Principal Component Analysis), KPCA (Kernel Principal Component Analysis), and KSPCA (Kernel Sparse Principal Component Analysis) are highly valuable for analyzing and identifying diverse fault types—including electronic component failures or mechanical system malfunctions. PCA stands as one of the most widely used methods in this domain due to its ability to capture dominant variations and patterns within datasets, which facilitates the detection of anomalies or failures. Implementations commonly involve eigenvalue decomposition of covariance matrices to reduce dimensionality while retaining critical information. DPCA and KPCA offer enhanced performance when standard PCA proves inadequate. DPCA extends PCA by incorporating time-lagged variables, making it suitable for dynamic process monitoring. KPCA leverages kernel functions to handle nonlinear data structures, projecting data into higher-dimensional spaces where linear separability is possible. KSPCA further advances fault diagnosis by integrating sparsity constraints with kernel-based approaches, enabling effective handling of highly nonlinear and high-dimensional data where traditional methods fall short. In summary, these techniques deliver strong practical outcomes for fault identification, diagnosis, and classification across various industrial scenarios.