Automated monitoring of large-scale complex-systems, such as cyber and transportation networks, requires characterising and modelling the extreme events that can occur in these networks, such as malware attacks and road closures. Such systems are 'multivariate', i.e. their performance is dependent on multiple interacting variables. Through the availability of new data sets from various sources on these systems, the project aims to characterise extreme events more coherently, and develop new methodology to model them.

Explaining the science

Joint modelling of multivariate (multiple variable) extremes across time, space, and networks is crucial for characterising extreme behaviour in complex transportation and cyber systems.

Safety regulations typically require engineers to design complex systems such that they can cope with certain extremes, and such regulations are typically formulated in terms of so called 'return levels'. The 'n-year return level' is the level that is so extreme it is expected to occur only once in every n years. Estimation of return levels in multivariate settings is a crucial task in transportation and cyber systems. The presence of non-stationary data (i.e. where the means and variances of the data change over time) in these applications is another challenge.

The availability of various covariate information (related, independent variables) in the cyber and the transportation applications can be exploited to help better characterise extreme events and dependent variables. This in turn helps to estimate return levels more accurately. Also the availability of large data sets enables the development of data-driven methodology for estimating highly extreme return levels with quantified uncertainty.

Project aims

The main aim of the project is to develop novel methodology, with theoretical guarantees, that models extreme events arising from large-scale and complex cyber and transportation networks.

The successful application of these methodologies will help in the systematic understanding of extreme behaviours in the complex systems mentioned and will provide improved prediction and uncertainty estimation for spatial and temporal anomalies.

These models and methods have the potential to address the highly challenging task of conducting automatic monitoring and mitigation of high consequence events in cyber and transportation networks, enhancing heir security and performance. 

This project is part of the Data-centric engineering programme's Grand Challenge of 'Monitoring Complex Systems'.


The new methodology developed in this work, along with that being conducted in the other project contributing to the Grand Challenge of 'Monitoring Complex Systems', could benefit cyber security, the transportation industry and could help to mitigate environmental hazards in complex engineering systems.


Researchers and collaborators