Digital Twins-A new paradigm for water supply and distribution networks

[EN] A digital twin (DT) is a virtual copy (a digital model) of a real system continuously fed with data to mimic the systems¿ past, present and future behaviour. This makes it possible to detect anomalies, test new ideas and changes in the virtual system and assess how it reacts, minimizing the risks to the real system. In this sense, the DT can be seen as a playground to explore the effects of different scenarios and to practice how to best react and operate the physical system under these circumstances. The concept of DT has been used traditionally in the industry field but it can also be developed and exploited in a city management context, and in particular in Water Supply and Distribution Networks (WSDN), where it can be applied to all aspects of the system.Martínez Alzamora, F.; Conejos Fuertes, MP.; Castro-Gama, M.; Vertommen, I. (2021). Digital Twins - A new paradigm for water supply and distribution networks. Hydrolink Magazine. 2:48-54. http://hdl.handle.net/10251/1901594854

Water Demand Uncertainty: The Scaling Laws Approach

The robust design of WDS has gained popularity over the last years. Researchers have been focusing on methods and algorithms to solve the stochastic optimization problems, and great improvements have been made in this aspect. However, the quantification of the uncertainty itself has not been addressed. Values for the variance and correlation of nodal demands are always assumed and no attention is being paid in properly quantifying these parameters. The optimization problems could be significantly improved if more realistic values for the uncertainty would be taken into account. This work addresses the need to understand in which measure the statistical parameters depend on the number of aggregated users and on the temporal resolution in which they are estimated. It intends to describe these dependencies through scaling laws, in order to derive the statistical properties of the total demand of a group of users from the features (mean, variance and correlation) of the demand process of a single-user. In future stages the results of this work will be incorporated in decision models for design purpose or scenario evaluation. Through this approach, we hope to develop more realistic and reliable WDS design and management solutions

Joint probabilities of demands on a water distribution network: A non-parametric approach

This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN.This paper proposes aprocedure to determine the probability of a specific water demand scenario in a Water Distribution Network (WDN). Stochastic correlated demands are generated for each node of the network using scaling laws. In particular, each demand fits a normal probability density function (PDF). To determine the joint probability of water demands at all nodes of the network, each nodal demand is divided in class intervals and a multidimensional contingency table is built. The joint probability represents the occurrence probability of a specific water demand scenario. The presented approach produces valuable information about demand scenarios and their probability of occurrence in a network. This method can find a further application in the robust optimization models for the design and management of WDN

Demand uncertainty in modelling water distribution systems

Water demand, that is perhaps the main process governing Water Distribution Systems (WDS), is affected by natural variability. The inherent uncertainty of demand is not negligible. Thus, uncertain demand should be modelled as a stochastic process or described using statistical tools. The stochastic modelling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal scales. At this aim, this paper presents a stochastic description of demand and discusses in which measure its statistical properties depend on the level of spatial and temporal aggregation. The analytical equations, expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users, namely the ‘scaling laws’, are theoretically derived and discussed. These relationships have reference to the mean-variance scaling or Taylor’s power law. The scaling laws are also validated using real water demand data of residential users. Through the scaling laws the statistical properties of the overall demand at each node of the WDS can be derived and the direct simulation of overall nodal demands can be done, reducing, among other things, the computational time in modelling or performing Monte Carlo Sampling of these systems

Scaling properties of water demand in design and management of water distribution systems

Water demand, that is perhaps the main process governing Water Distribution Systems (WDS), is affected by natural variability. The inherent uncertainty of demand is not negligible. Thus, uncertain demand should be modelled as a stochastic process or characterized using statistical tools. The stochastic modelling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal scales. At this aim, this paper presents a stochastic description of demand and discusses in which measure its statistical properties depend on the level of spatial and temporal aggregation. The analytical equations, expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users, namely the scaling laws, are theoretically derived and discussed. Hereafter the scaling laws are validated using real water demand data of residential users and synthetic demand series generated by a non-homogeneous Poisson Rectangular Pulse (PRP) process. Through the scaling laws the statistical properties of the overall demand at each node of the WDS can be derived and the direct simulation of overall nodal demands can be done, reducing, among other things, the computational time in modelling these systems.Water demand, that is perhaps the main process governing Water Distribution Systems (WDS), is affected by natural variability. The inherent uncertainty of demand is not negligible. Thus, uncertain demand should be modelled as a stochastic process or characterized using statistical tools. The stochastic modelling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal scales. At this aim, this paper presents a stochastic description of demand and discusses in which measure its statistical properties depend on the level of spatial and temporal aggregation. The analytical equations, expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users, namely the scaling laws, are theoretically derived and discussed. Hereafter the scaling laws are validated using real water demand data of residential users and synthetic demand series generated by a non-homogeneous Poisson Rectangular Pulse (PRP) process. Through the scaling laws the statistical properties of the overall demand at each node of the WDS can be derived and the direct simulation of overall nodal demands can be done, reducing, among other things, the computational time in modelling these systems

Scaling Water Consumption Statistics

The authors acknowledge the publisher in granting permission for making post-print version available in open access institutional repository.Water consumption is perhaps the main process governing water distribution systems. Because of its uncertain nature, water consumption should be modeled as a stochastic process or characterized using statistical tools. This paper presents a description of water consumption using statistics as the mean, variance, and correlation. The analytical equations expressing the dependency of these statistics on the number of served users, observation time, and sampling rate, namely, the scaling laws, are theoretically derived and discussed. Real residential water consumption data are used to assess the validity of these theoretical scaling laws. The results show a good agreement between the scaling laws and scaling behavior of real data statistics. The scaling laws represent an innovative and powerful tool allowing inference of the statistical features of overall water consumption at each node of a network from the process that describes the demand of a user unit without loss of information about its variability and correlation structure. This will further allow the accurate simulation of overall nodal consumptions, reducing the computational time when modeling network

Water demand uncertainty: the scaling law approach

The robust design of WDS has gained popularity over the last years. Researchers have been focusing on methods and algorithms to solve the stochastic optimization problems, and great improvements have been made in this aspect. However, the quantification of the uncertainty itself has not been addressed. Values for the variance and correlation of nodal demands are always assumed and no attention is being paid in properly quantifying these parameters. The optimization problems could be significantly improved if more realistic values for the uncertainty would be taken into account. This work addresses the need to understand in which measure the statistical parameters depend on the number of aggregated users and on the temporal resolution in which they are estimated. It intends to describe these dependencies through scaling laws, in order to derive the statistical properties of the total demand of a group of users from the features (mean, variance and correlation) of the demand process of a single-user. In future stages the results of this work will be incorporated in decision models for design purpose or scenario evaluation. Through this approach, we hope to develop more realistic and reliable WDS design and management solutions

WATER DISTRIBUTION NETWORK SIMULATION WITH THE USE OF SCALING LAWS

Water demand, that is perhaps the main process governing Water Distribution Systems (WDS), is affected by natural variability. The inherent uncertainty of demand is not negligible. Thus, uncertain demand should be modelled as a stochastic process or characterized using statistical tools. The stochastic modelling of water demand requires knowledge of the statistical features of the demand time series at different spatial and temporal scales. At this aim, this paper presents a stochastic description of demand and discusses in which measure its statistical properties depend on the level of spatial and temporal aggregation. The analytical equations, expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users, namely the scaling laws, are theoretically derived and discussed. The scaling laws are validated using real water demand data of residential users and through a simple network simulation. Through the scaling laws the statistical properties of the overall demand at each node of the WDS can be derived and the direct simulation of overall nodal demands can be done, reducing, among other things, the computational time in modelling these systems

Robust Design of a Real-Life Water Distribution Network under Different Demand Scenarios

In this paper a scenario-based robust optimization approach is proposed to take demand uncertainty into account in the design of water distribution networks. This results in insight in the trade-off between costs and performance of different designs. Within the proposed approach the designer is able to choose the desired degree of risk aversion, and the performance of the design can be assessed based on the water demand effectively supplied under different scenarios. Both future water demand scenarios and scenarios based on historical records are considered. The approach is applied to the design of a real-life water distribution network supplying part of a city in the Netherlands. From the results the relation between costs and performance for different scenarios becomes evident: a more robust design requires higher design costs. Moreover, it is proven that numerical optimization helps finding better design solutions when compared to manual approaches. The developed approach allows water utilities to make informed choices about how much to invest in their infrastructure and how to design it in order to achieve a certain level of robustness