The need to monitor and control technical systems and processes has existed since the early beginnings of the industrial revolution back in 19th century. However, with the permanent increase in size and complexity of the modern technical systems, both control and monitoring tasks have become very demanding and challenging. This is one of the reasons why has fault diagnosis as a specific monitoring task received so much attention from the research community in the last four decades. The fault diagnosis process considered in this thesis has been separated into two causally related steps: fault detection and fault isolation. Because all fault isolation algorithms utilize some form of structural analysis, they all face the problem of isolability. The lack of isolability in the model structures used for fault isolation inevitably leads to inaccurate fault isolation results. Moreover, the size of model structures used for fault isolation in the contemporary complex technical processes makes the fault isolation computationally challenging.