Resumen de Comprehensive approach for on-line monitoring water distribution systems via state estimation related techniques
Sarai Díaz García
Water distribution systems (WDS) are currently being modernised with Information Communication Technologies (ICT) that aim to on-line monitor the water mains. This specifically requires the installation of telemetry systems that collect real-time information provided by the metering devices distributed throughout the network. However, the potential of computerised telemetry can only be developed if appropriate data processing techniques are used to infer the hydraulic variables from the available isolated data. State estimation (SE) techniques were developed in the 1970s by the power supply industry with this purpose, and have now become essential tools in the field. They have also been discussed in the water domain on an academic and scientific level since the early 1980s, but they have hardly been implemented in real-life water networks on an operational level. This limits the possibilities of the recent boost on ICT in WDS all over the world, which demands practitioners and researchers to make the most of the huge amount of on-line data available.
In order to squeeze the millionaire investments in technology systems, it is firstly required to efficiently adapt SE techniques and other related complementary analyses (e.g. observability analysis, uncertainty evaluation) to the reality of WDS. Nevertheless, such adaption on its own is not enough to take full advantage of telemetry systems. In order to achieve full potential, implementation of SE monitoring tools also demands to comprehensively address some other real-time issues that are currently source of concern for the water industry (e.g. calibration, leak detection, topological identification, among others). Up to this date, these problems have been tackled individually, but only by unifying the approach to all WDS analysis applications is possible to extract useful information for the on-line control of water networks. The paradigm of WDS needs to be adapted to the reality of ICT, and SE related techniques are a good alternative to embrace the change. This PhD thesis presents a unified comprehensive approach for on-line monitoring WDS via SE related techniques. With this aim, the present work gathers eight methodological contributions conceived to (1) ensure that SE results are reliable, and (2) extract as much information as possible from SE results to enhance the real-time operation of water networks.
Firstly, methodologies are here presented to address the observability analysis (OA) problem, which consists on assessing if sufficient measurements exist to infer the hydraulic state of the system in a subsequent SE process based on the available measurements. More specifically, an algebraic and a stochastic approach are developed. The algebraic method consists on applying a gauss-based elimination technique to the so called measurement Jacobian matrix, whereas the stochastic methodology assesses observability by comparing the uncertainty of the hydraulic variables when assuming random gaussian distributions and when considering the existence of error-free metering devices. Also, a robust method to evaluate SE uncertainty even when hydraulic constraints, high precision measurements and lower and upper variable bounds exist is presented, and explicit expressions are derived to compute SE sensitivity analysis with respect to both measurements and model parameters by perturbing the Karush-Kuhn-Tucker (KKT) conditions. These techniques enable to efficiently assess the quality of the state estimate, thus permitting to determine if the system is suitable for the real-time implementation of SE techniques.
On the other hand, several traditional WDS analysis applications are here addressed from a SE perspective. A procedure to calibrate WDS via multi-period SE is developed by applying mathematical programming decomposition techniques to the combined parameter and state estimation problem. Also, a methodology to assess the observability of such an approach is presented. Then, a probabilistic method for leak detectability assessment via SE is provided. This approach assumes that leaks can be detected as erroneous measurements, hence the largest normalised residual test can be used for leakage awareness purposes. Moreover, the probability of leak detection is here computed by working with the measurement-estimate joint bivariate variance-covariance matrix rather than undertaking sampling experiments, and minimum leak value maps are easily plotted to show the network possibilities in terms of real-time leak detectability. Finally, OA and SE are adapted in this work to deal with changing network topologies. Topological observability analysis (TOA) is here presented as an analysis that permits to assess if sufficient algebraic relationships exist to infer in a subsequent topological state estimation (TSE) process both the hydraulic state and the status of the pumps and valves within the network from the available measurement setting. This approach permits to make different assumptions about the available information for each specific pump or valve by making slight amendments to the Jacobian matrix, which is the basis for standard OA methods. The TSE methodology formulates the presence of such pumps and valves with binary variables, which have to be inferred from the noisy measurement setting together with the rest of hydraulic variables. The original mixed integer non-linear programming (MINLP) problem is here solved with an iterative mixed integer quadratic programming (MIQP) approach by linearizing some hydraulic constraints.
Results show that reliable SE can be undertaken once the observability capabilities of WDS have been explored and the effect of measurement noise has been conveniently assessed. Additionally, the aforementioned methodologies for calibration, leak detectability and TSE have been confirmed to work well, thus successfully giving answer to some traditionally independent problems with a common philosophy. Further work is needed on several related real-time applications, but this thesis proves that a comprehensive approach for on-line monitoring WDS via SE techniques is possible. Moreover, it is a real need in order to take full advantage of the huge amount of information currently provided by ICT platforms.
