In modern process industries, frequent changes in
operating conditions often result in process data exhibiting
complex multi-modal distributions. Traditional fault detection
methods struggle to generalize to newly emerging operating
modes due to limited data samples. Additionally, real-world
industrial data are prone to anomalies caused by sensor faults or
environmental disturbances. To address these issues, this paper
introduces a shared-private subspace decomposition mechanism
and a sample-level weighting strategy based on the traditional
Mixture of Probabilistic Principal Component Analysis (MPPCA)
model. A fault detection model based on this method is designed,
and industrial case studies demonstrate its ability to effectively
extract global structural features from multi-modal process data,
showing significant advantages in fault detection tasks under
zero-shot and noisy scenarios in new operating conditions.