Fluid systems, which include urban water distribution and sewage systems, are responsible for up to 8\% of energy consumption in the European Union. At the same time, they are susceptible to disruptions. Using mathematical optimisation methods, urban water distribution systems can be designed and operated to be both more energy efficient and more resilient, although resilience and energy efficiency are often at odds. The selection of suitable functions for the evaluation of these system properties is often the central challenge in modelling. As complex supply systems, urban infrastructure systems often require a holistic view and modelling at system level. When modelling, we are guided by the TOR methodology.

The generic term agent summarises various concepts. We understand an agent to be an autonomous unit whose goals or knowledge differ from other agents in the system. These units together form a multi-agent system in a common environment. The research field of multi-agent systems is as diverse as its term definition, forming the intersection between concepts from game theory, computer science (e.g. reinforcement learning) and the social sciences.

We investigate whether multi-agent systems can be used to operate distributed systems (such as water distribution systems) efficiently, i.e. close to a mathematical optimum, with less expert knowledge than mathematical optimisation would require. In order to be able to control technical systems with a multi-agent approach, the agents must be able to perceive their environment and communicate with each other. We are investigating this in simulations and on a test rig in various research projects.

Conventional control of technical systems uses feedback to monitor the value of a controlled variable and to react in the event of a deviation from the setpoint, i.e. to adjust the controlled variable so that the deviation is eliminated.

We use methods of time series analysis, some of which are borrowed from economic sciences, to develop controllers that can learn from disturbances and anticipate hazards. To do this, we can model the signal of the controlled variable as an ARIMA process, for example. The model is learnt by a controller and the setpoint is adjusted so that functional losses can be reduced.

The performance of these signal-based control methods must be assessed in comparison with conventional control and model-based control. The signal-based methods offer the advantage that the modelling effort is reduced. In addition, there is often not enough data available to create a comprehensive model of the system, especially in urban water supply systems.

According to the United Nations, the current trends in urbanization and simultaneous global population growth will result in an additional 2.5 billion people living in urban areas, equivalent to 68% of the entire global population. Water supply system is an important component of the infrastructure that does not only provide water to citizens, but also to industry, agriculture and electricity generation systems.

Within a research project funded by the KSB Foundation, machine learning methods are to be developed in order to anticipate water demand in urban areas subject to rapid urbanization. The existing water supply infrastructure will be adjusted in accordance with the predicted demand by mathematical optimization. This adjustment will be performed under the consideration of the cost-benefit analysis and water network resilience metrics. To achieve this, graph-theoretical resilience metrics will be used and extended according to new findings. Moreover, an analysis of various urban structures and their influence on the resilience of their water supply infrastructure will be studied. This should lead to recommendations for guiding urban development of future cities.

The majority of the world's population lives in cities. In Germany, the proportion of the urban population is expected to reach 85 % by 2050. These people are highly dependent on urban infrastructure. At the same time, cities and their infrastructure, which is increasingly supported by digital technologies, are vulnerable to critical events, e.g., resulting from the consequences of climate change, the frequency and intensity of which will continue to increase. The LOEWE centre emergenCITY is developing solutions to make our cities resilient and safe even in the event of crises.

We are part of the interdisciplinary team of emergenCITY and focus on the resilience of urban water distribution systems. In this context, we further develop methods for resilience assessment and use mathematical optimisation methods for the design of resilient water distribution systems.

In addition to design, operation also plays an important role in achieving resilience. This is why we use time series analysis methods to monitor systems, respond to hazards and learn from disruptions in order to anticipate new hazards. We develop control algorithms that can fulfil these functions. The algorithms are validated using an experimental setup .

We collaborate with our colleagues from other disciplines to utilise analogies between water and electricity supply and to consider interdependencies between different urban systems, to develop historically informed models of the population's behaviour in the event of a disaster and to transfer innovative methods of control with which the population's behaviour can be taken into account in the control strategy for water distribution systems. In addition, we are involved in the interdisciplinary Mission Knowledge Base, which investigates the benefits of urban data platforms for disaster management in cities.

Around one billion people worldwide live in slums, often without urban infrastructure such as electricity or water. To change this, the number of inhabitants and their development must first be known. To do this, slums in several cities are recorded at different times using satellite data. Then it will be investigated whether their development can be described with simple mathematical models such as those otherwise used to describe physical processes. Such new data-driven models could be used to understand how slums, and especially the needs of the people who live in them, will develop in the future.

The project is supervised by Dr.-Ing. John Friesen and Nicolas Kraff .

The function of technical infrastructure is dependent on human demand behavior. Especially in times of uncertainty and crisis, it is important to know and understand the state and behavior of this socio-technical system. We research how digital twins can be utilized for this challenge. We use physical, data driven and agent-based models for the behavior and interaction of humans and infrastructure.

The project is supervised by Jonathan Sattler. He is a research associate at the Institute for the Protection of Terrestrial Infrastructures of the German Aerospace Center (DLR) and an external doctoral student at FST.

Water management in Germany is neither resource-efficient nor does it meet the needs of the various stakeholders: Drought can lead to gaps in supply, operation is not energy-optimised and changes to the supply network are time-consuming and costly. In order to address these challenges, new, adaptive and resource-saving operating strategies for the water infrastructure are required. Data-based artificial intelligence methods and heuristic approaches harbour considerable potential for this. However, there are immediate questions regarding the availability of the necessary data and the traceability and transparency of the approaches.

Another option is to use market-based mechanisms. With an adequate market design, the inherent resource and allocation efficiency of the market can be utilised to achieve comprehensible, resource-efficient and demand-oriented operating strategies.

As part of agents42watermarkets, we are focussing on the development and testing of these operating strategies of the future, in which physical components act autonomously as agents within a predefined framework.