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Data based monitoring methods are often utilized to carry out fault detection (FD) when process models may not necessarily be available. The partial least square (PLS) and principle component analysis (PCA) are two basic types of multivariate FD methods, however, both of them can only be used to monitor linear processes. Among these extended data based methods, the kernel PCA (KPCA) and kernel PLS (KPLS) are the most well-known and widely adopted. KPCA and KPLS models have several advantages, since, they do not require nonlinear optimization, and only the solution of an eigenvalue problem is required. Also, they provide a better understanding of what kind of nonlinear features are extracted: the number of the principal components (PCs) in a feature space is fixed a priori by selecting the appropriate kernel function. Therefore, the objective of this work is to use KPCA and KPLS techniques to monitor nonlinear data. The improved FD performance of KPCA and KPLS is illustrated through two simulated examples, one using synthetic data and the other using simulated continuously stirred tank reactor (CSTR) data. The results demonstrate that both KPCA and KPLS methods are able to provide better detection compared to the linear versions.

Chemical industries focus primarily on profitable operations, resulting in growing attention and advances in the field of digital twins and optimal control algorithms.However, most industries still struggle due to a lack of physical sensors, infrequent measurements, and asynchronous sampling. Thus, in this work, we have designed a multi-rate state observer for state estimation from plant measurements and developed a model predictive controller (MPC) that maximized the profitability of an industry-scale fermentation process (fermenter volume < 378,500 L).Additionally, as the fermentation process is complex due to the use of microorganisms, which cannot be accurately captured using a first-principles model, we utilize a previously developed hybrid model in the proposed MPC formulation.The MPC uses a GAMS-MATLAB framework to determine the optimal input profiles while considering practical process constraints. It is shown using multiple datasets, that the MPC can increase productivity while also decreasing the plant operating cost.