The steadily increasing demand for optimal and safe operation of technological processes drives the need for their close monitoring and supervision. This leads to process monitoring steadily gaining more and more attention within newly deployed plants. As the underlying methods aim to detect and isolate occurring faults both fast and precisely, overcoming associated computational complexity becomes a challenging task.



This work introduces a set-based framework for model-based fault detection and isolation for discrete-time systems. The framework allows to consider hybrid polynomial systems subject to bounded uncertainties in parameters, states or measurement data. The goal is to determine situations where irregularities in the measurement data are not explained by the known uncertainties, i.e. they are an indication of an occurred fault. The proposed method combines polynomial hybrid dynamics with unknown-but-bounded data in form of general semi-algebraic inequalities into one feasibility problem.



The challenge of computational complexity is approached in this thesis in two ways: First, defining diagnosability via output reachable sets allows to offload the required computations and implement an online notification procedure based on measurement quantization. Second, several approaches to reduce problem formulation are introduced, exploiting model structure and tailoring to specific problem classes.