Report on Hydroinformatics 2004, Singapore

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Using a multi-objective genetic algorithm for SVM construction

Support Vector Machines are kernel machines useful for classification and regression problems. In this paper, they are used for non-linear regression of environmental data. From a structural point of view, Support Vector Machines are particular Artificial Neural Networks and their training paradigm has some positive implications. In fact, the original training approach is useful to overcome the curse of dimensionality and too strict assumptions on statistics of the errors in data. Support Vector Machines and Radial Basis Function Regularised Networks are presented within a common structural framework for non-linear regression in order to emphasise the training strategy for support vector machines and to better explain the multi-objective approach in support vector machines' construction. A support vector machine's performance depends on the kernel parameter, input selection and ε-tube optimal dimension. These will be used as decision variables for the evolutionary strategy based on a Genetic Algorithm, which exhibits the number of support vectors, for the capacity of machine, and the fitness to a validation subset, for the model accuracy in mapping the underlying physical phenomena, as objective functions. The strategy is tested on a case study dealing with groundwater modelling, based on time series (past measured rainfalls and levels) for level predictions at variable time horizons

Using genetic programming to determine Chèzy resistance coefficient in corrugated channels

Genetic Programming has been used to determine Chèzy resistance coefficient for full circular corrugated channels. Three corrugated plastic pipes have been experimentally studied in order to generate data. The tests aim at measuring hydraulic parameters of the open-channel flow for some slopes, from 3.49–17.37% (2–10°), in order to discover the dependence of the channel resistance coefficient when wake-interference flow occurs. The monomial formula for the Chèzy resistance coefficient performs well on experimental data, both from measurement errors and from a technical point of view. In this paper, we present some very parsimonious formulae that have been created by Genetic Programming with few constants and which fit the data better than the monomial formula. Moreover, two of the Genetic Programming formulae, after 'physical post-refinement', seem to better explain the role of the roughness in the Chèzy resistance coefficient for corrugated channels with respect to its traditional expression for rough channels. This fact suggests that at least the structure of those formulae can be extrapolated to other types of corrugated channels. Finally, the work stresses the fact that the Genetic Programming hypothesis can be easily manipulated by means of 'human' physical insight. Therefore, Genetic Programming should be considered more than a simple data-driven technique, especially when it is used to perform scientific discovery

Testing linear solvers for global gradient algorithm

Steady-state Water Distribution Network models compute pipe flows and nodal heads for assumed nodal demands, pipe hydraulic resistances, etc. The nonlinear mathematical problem is based on energy and mass conservation laws which is solved by using global linearization techniques, such as global gradient algorithm (GGA). The matrix of coefficients of the linear system inside GGA belongs to the class of sparse, symmetric and positive definite. Therefore a fast solver for the linear system is important in order to achieve the computational efficiency, especially when multiple runs are required. This work aims at testing three main strategies for the solution of linear systems inside GGA. The tests are performed on eight real networks by sampling nodal demands, considering the pressure-driven and demand-driven modelling to evaluate the robustness of solvers. The results show that there exists a robust specialized direct method which is superior to all the other alternatives. Furthermore, it is found that the number of times the linear system is solved inside the GGA does not depend on the specific solver, if a small regularization to the linear problem is applied, and that pressure-driven modelling requires a greater number which depends on the size and topology of the network and not only on the level of pressure deficiency

Roland K. Price & Zoran Vojinovic Urban Hydroinformatics: Data, Models and Decision Support for Integrated Urban Water Management by January 2011. IWA Publishing, London. 552 pages. Paperback ISBN: 9781843392743, £105.00/US$189.00/€ 141.75

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Water distribution network calibration using enhanced GGA and topological analysis

The calibration of hydraulic models of water distribution networks (WDN) is of preeminent importance for their analysis and management. It is usually achieved by solving a constrained optimization problem based on some priors on decision variables and the demand-driven simulation of the entire network, given the observations of some hydraulic status variables (i.e. typically nodal heads and sometimes pipe flows). This paper presents a framework to perform the calibration of pipe hydraulic resistances considering two main issues: (i) the enhancements of WDN simulation models allowing us to simplify network topology with respect to serial nodes/trunks and/or to account for a more realistic representation of distributed demands and (ii) a different formulation of the calibration problem itself. Depending on the available measurements, the proposed calibration strategy reduces the hydraulic simulation model size and can permit the decomposition of the network. On the one hand, such a procedure allows for numerical and computational advantages, especially for large size networks. On the other hand, it allows a prompt analysis of observability of calibration decision variables based on actual observations and might help identifying those pipes (i.e. hydraulic resistances) which are more important for the whole network behaviour

Modularity Index For The Segmentation Of Water Distribution Networks

The search for suitable segmentations is a challenging issue for analysis, planning and management of water distribution networks (WDNs). In fact complex and large size hydraulic systems require the division into modules in order to simplify the analysis and the management tasks. In complex network theory, modularity index was proposed as a measure of the strength of the network division into communities. Nevertheless, modularity index needs to be revised considering the specificity of the hydraulic systems. Accordingly, the classic modularity index is firstly presented and, then, tailored and modified for WDNs. Furthermore, a multi-objective strategy for optimal segmentation is presented. The optimization framework is based on the maximization of the WDN-oriented modularity-based index versus the minimization of the cost of newly installed devices in order to segment WDNs

Advances in data-driven analyses and modelling using EPR-MOGA.

Evolutionary Polynomial Regression (EPR) is a recently developed hybrid regression method that combines the best features of conventional numerical regression techniques with the genetic programming/symbolic regression technique. The original version of EPR works with formulae based on true or pseudo-polynomial expressions using a single-objective genetic algorithm. Therefore, to obtain a set of formulae with a variable number of pseudo-polynomial coefficients, the sequential search is performed in the formulae space. This article presents an improved EPR strategy that uses a multi-objective genetic algorithm instead. We demonstrate that multi-objective approach is a more feasible instrument for data analysis and model selection. Moreover, we show that EPR can also allow for simple uncertainty analysis (since it returns polynomial structures that are linear with respect to the estimated coefficients). The methodology is tested and the results are reported in a case study relating groundwater level predictions to total monthly rainfall

Calibration of Design Models for Leakage Management of Water Distribution Networks

AbstractWater losses in urban water distribution networks (WDN) accelerate the deterioration of such infrastructures. The enhanced hydraulic modelling provides a phenomenological representation of WDN hydraulics, including the modelling of leakages as function of pipe average pressure and deterioration. The methodological use of such models on real WDN was demonstrated to support the planning of leakage management actions. Nonetheless, many water utilities are still in the process of designing flow/pressure monitoring, thus data available are not enough to perform detailed calibration of such models.This work presents a physically based approach for the calibration of WDN hydraulic models aimed at supporting leakage management plans since early stages. The proposed procedure leverages the key role of mass balance in enhanced hydraulic models and the technical insight on pipe deterioration mechanisms for various quantity and quality of available data. Two calibration studies of real WDNs demonstrate the feasibility of the approach and show that the distribution of leakages in the WDN does not much influence the pressure values, which confirms the need for flow measurements at monitoring districts for leakage and asset management