Modern society relies heavily on the availability and smooth operation of large-scale complex engineering systems such as electrical power systems, water distribution systems, telecommunication networks and transportation systems. These are called critical infrastructure (CI) systems and a major part of our everyday life depends on their reliable and secure operation. A CI system failure can occur due to faults (e.g. equipment faults, human error, software bugs), natural disasters or malicious attacks and it can have severe societal, health and economic consequences. As the demand for CI services is growing rapidly, these systems become larger, more complex and have evolved into heterogeneous and distributed infrastructures. This has created interdependencies between them, with fault effects propagating to interdependent infrastructures. In fact, when multiple faults occur simultaneously, a high impact cascading failure could occur. For example, in November 2006, a local fault in Germany's power grid cascaded through large areas of Europe resulting in 10 million people left without electricity in Germany, France, Austria, Italy, Belgium and Spain. Considering such severe consequences of undetected cascading failures due to faults, it is crucial that a fault diagnosis engine must make online, real-time decisions and continuously improve and adapt to the sequential arrival of data. The overall objectives of the fellowship are to design and develop novel online learning algorithms with adaptation capabilities, with an application focus on real-time monitoring of CI systems, to accurately detect a potential fault and effectively isolate its exact location.