The Monitoring technique plays a vital role in ensuring the proper functioning of modern industrial systems that are highly sophisticated and automated. On two different applications, this thesis investigates two major categories of information redundancy monitoring techniques, model-based and data-driven.

The first application focuses on ground fault detection in microgrid systems. Leveraging the model information of the system, we propose a design approach for the fault detection filter by creating a linear programming problem. This design ensures the complete decoupling of the disturbance and guarantees fault sensitivity. Recognizing that decoupling is not always feasible, we create a new optimization problem by exploiting available disturbance patterns, so that the filter suppresses the impact of the disturbances while ensuring the fault sensitivity. Simulation studies validate the effectiveness of the proposed designs. The second application deals with non-intrusive load monitoring (NILM) in building systems. Our approach involves a two-stage process that utilizes data to perform NILM. In the first stage, events are identified from the aggregate load measurement. In the second stage, an integer programming problem is formulated to estimate the load for each appliance. The effectiveness of our method is evaluated on a real-world dataset and compared with several other NILM approaches, demonstrating competitive performance in terms of accuracy and computational complexity.