Industrial processes are nonlinear and complicated, requiring accurate fault identification to minimize performance deterioration and respond quickly to emergencies. This work investigates industrial process defect identification and isolation, which is analytically difficult owing to their complexity. This paper carefully analyzes four design methods for flaw identification and isolation based on Principal Component Analysis (PCA), Fisher Discriminant Analysis (FDA), Kernel Fisher Discriminant Analysis (KFDA), and Sequential quadratic programming (SQP). Our study includes the Tennessee Eastman Process (TEP) and the Penicillin Fermentation Process (PFP), among other comparable methods. We assess the proposed fault detection and isolation methods through detailed analysis and comparison. The simulation findings from our extensive investigation provide remarkable insights. Simulation findings show that FDA and KFDA work well in fault identification and isolation, but PCA has certain limits. We also considered SQP as a TEP fault detection and isolation improvement tool. SQP is noted for its success in nonlinear and restricted optimization problems, making it ideal for fault identification and isolation in complicated industrial processes. Data-driven design approaches increase problem identification in complicated industrial processes with greater reliability and efficiency than PCA-based methods. This study also shows that advanced data-driven techniques can improve industrial fault diagnosis, improving operational safety and system performance by leveraging the FDA, KFDA, and SQP.