This chapter introduces three distinct frameworks for industrial system monitoring and prediction, aiming at enhancing the performance of Fault Detection and Diagnosis (FDD), prediction of Key Performance Indicators (KPIs) in large-scale industrial systems and multimode process monitoring. First, a multigroup fault detection and diagnosis framework for large-scale nonlinear industrial systems using nonlinear multivariate analysis is proposed to deal with the nonlinear variable relationships, improving the detection of minor faults, and revealing fault shifts between variables and groups. Then, a new approach termed VBGMM-CCA for multimode process monitoring is introduced, which integrates the Variational Bayesian Gaussian Mixture Model (VBGMM) with Canonical Correlation Analysis (CCA) to effectively monitor the multimode processes. Finally, a two-stage multi-target domain adaptation framework (TS-MAAN) for predicting KPIs under uncommon operating conditions is presented, which leverages knowledge from common conditions to build predictive models. These methods all demonstrate potential for practical application in their respective fields.