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EVOLUTIONARY ALGORITHM AND EXPECTATION
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MAXIMISATION STRATEGIES FOR IMPROVED DETECTION OF
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PIPE BURSTS AND OTHER EVENTS IN WATER DISTRIBUTION
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SYSTEMS
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Romano, M., Kapelan, Z., and Savić, D. A.
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Abstract
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A fully automated data-driven methodology for the detection of pipe bursts and other events which
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induce similar abnormal pressure/flow variations (e.g., unauthorised consumptions) at the District
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Metered Area (DMA) level has been recently developed by the authors. This methodology works by
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simultaneously analysing the data coming on-line from all the pressure and/or flow sensors deployed
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in a DMA. It makes synergistic use of several self-learning Artificial Intelligence (AI) and statistical
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techniques. These include: (i) wavelets for the de-noising of the recorded pressure/flow signals, (ii)
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Artificial Neural Networks (ANNs) models for the short-term forecasting of pressure/flow signal
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values, (iii) Statistical Process Control (SPC) techniques for the short and long term analysis of the
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burst/other event-induced pressure/flow variations, and (ivi) a DMA level Bayesian Inference Systems
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(BISs) for inferring the probability that a pipe burst/other event has occurred in the DMA being
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studied and, raising the corresponding detection alarms, and provide information useful for
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performing event diagnosis. This paper focuses on the (re)calibration of the above detection
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methodology with the aim of improving the ANN models forecasting and the DMA level BIS
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classification performances of the ANN models and the classification performances of the BIS used to
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raise the detection alarms (i.e., DMA level BIS). This is achieved by using: (1) an Evolutionary
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Algorithm optimisation strategy for selecting the best ANN input structures and related parameter
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values to be used for training the ANN models, and (2) an Expectation Maximisation strategy for
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(re)calibrating the values in the Conditional Probability Tables (CPTs) of the DMA level BIS. The
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(re)calibration procedure is tested on a case study involving several UK DMAs in the United
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Kingdom (UK) with both real-life pipe bursts/other events, and engineered pipe burst events (i.e.,
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simulated by opening fire hydrants) and synthetic pipe burst events (i.e., simulated by arbitrarily
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adding “burst flows” to an actual flow signal). The results obtained illustrate that the new
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(re)calibration procedure improves the performance of the event detection methodology in terms of
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increased detection speed and reliability.
Michele Romano, Centre for Water Systems, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison
Building, North Park Road, Exeter, Devon, EX4 4QF, United Kingdom, Email: mr277@exeter.ac.uk (corresponding author)
Zoran Kapelan, Centre for Water Systems, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison
Building, North Park Road, Exeter, Devon, EX4 4QF, United Kingdom, Email: Z.Kapelan@exeter.ac.uk
Dragan A. Savić, Centre for Water Systems, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison
Building, North Park Road, Exeter, Devon, EX4 4QF, United Kingdom, Email: D.Savic@exeter.ac.uk
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INTRODUCTION
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Pipe burst events in Water Distribution Systems (WDSs) are a compelling issue for the water
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companies worldwide as the loss of large volumes of treated and frequently pumped water is
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environmentally and economically damaging. Furthermore, they have a negative impact on the water
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companies’ operational performance, customer service and reputation. Cost-effective reduction of
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water leakages caused by the pipe burst events is however a challenging task. New and more efficient
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methodologies are required for their timely and reliable detection of these events. This said, note that
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despite the fact that the pipe burst events only initiate the water leakages, in this paper the two terms
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are used interchangeably (as it is often done in engineering practice).
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Despite its importance, the detection of pipe burst events is one of the tasks faced by the water
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companies that is becoming more and more difficult. The main reasons for this are the increasing
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complexity of the WDSs, the fact that water companies are starting to routinely implementing
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pressure management programmes, and the installation of more and more poly-ethylene pipes (on
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which the conventional, acoustic equipment-based techniques do not work that well). As a result, in
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many cases, pipe bursts are brought to the attention of a water company only when someone calls in
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to report a visible event.
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A fully automated, data-driven methodology for the near real-time detection of pipe bursts and other
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events at the District Metered Area (DMA) level has been recently developed (Romano et al. 2012).
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This methodology is implemented in a fully automated Event Recognition System (ERS) which works
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by simultaneously analysing the data coming on-line from all the pressure and/or flow sensors
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deployed in a DMA. It makes synergistic use of several self-learning Artificial Intelligence (AI) and
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statistical techniques. These include Artificial Neural Network (ANN) models for the short-term
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forecasting of pressure/flow signal values, and a DMA level Bayesian Inference System (BIS) for
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inferring the probability that a pipe burst/other event has occurred in the DMA being studied and
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raising the corresponding detection alarms. The objective of the work presented here is to develop a
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new methodology for the effective data-driven (re)calibration of the ERS by using: (1) an
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Evolutionary Algorithm optimisation strategy (Schwefel 1981) for improving the forecasting
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performance of the ANN models, and (2) an Expectation Maximisation strategy (Dempster et al.
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1977; Lauritzen 1995) for improving the classification performance of the DMA level BIS.
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This paper is organised as follows. After this introduction, relevant background information is
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presented in the next section. Then an overview of the ERS is given. This is followed by two sections
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presenting the theoretical background and methodological details of the Evolutionary Algorithm and
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Expectation Maximisation optimisation strategies, respectively. The latter sections constitute the core
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of the new contribution presented in this paper. Once this is done, the results of the (re)calibration
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methodology tests on several UK DMAs in the United Kingdom (UK) with both real-life pipe
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burst/other events, and engineered pipe burst events (i.e., simulated by opening fire hydrants) and
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synthetic pipe burst events (i.e., simulated by arbitrarily adding fictitious “burst flows” to an actual
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flow signal) Engineered Events (EEs) are presented in the case study section. Finally, the main
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conclusions are drawn and acknowledgements given.
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BACKGROUND
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Current solutions to the pipe burst events detection problem are based on various principles. A large
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group of techniques utilize utilises highly specialized hardware equipment. Techniques such as leak
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noise correlators (e.g., Grunwell and Ratcliffe 1981), gas injection (e.g., Field and Ratcliffe 1978),
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and pig-mounted acoustic sensing (e.g., Mergelas and Henrich 2005), belong to this group. Despite
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the fact that some of these techniques are the most accurate ones used today (Puust et al. 2010), they
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are expensive, labour-intensive, slow to run and may require the cessation of pipeline operations for
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long periods of time. Consequently, much research has been focussed on finding equally effective, but
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faster techniques that cost less to run.
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Several techniques exist that make use of transient analysis. These include inverse transient analysis
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(e.g., Liggett and Chen 1994) and frequency domain techniques (e.g., Mpesha et al. 2001). Other
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techniques from this group seek to exploit special features in the unsteady signal rather than infer the
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presence and location of a pipe burst by reproducing the transient trace in a simulator in the time or
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frequency domain (e.g., Brunone 1999; Kim 2005; Wang et al. 2002). The techniques in this group
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are potentially appealing due to their inexpensive and non invasive nature, good operational range,
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relative insensitivity to pipe characteristics (e.g., material and diameter), and sensor-to-sensor spacing
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required. However, transient analysis-based techniques require pressure and other measurements
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sampled with a high frequency and a significantly larger number of such sensors that are normally
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present in a pipeline system, thereby leading to increased costs. Also, these techniques often rely on
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complex and inaccurate transient network simulation models and require precise knowledge of the
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pipeline and instrumentation parameters. As a result, they have had limited success so far, generally
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on single pipelines only. Various steady state analysis-based techniques have also been developed
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(e.g., Pudar and Liggett 1992; Misiunas et al. 2006; Puust et al. 2006; Wu et al. 2010). Compared to
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the transient analysis-based techniques, these methods do not require the collection of data at high
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frequencies but seem to be reliant on the availability of an extensive number of accurate
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measurements. In addition, the availability of well calibrated hydraulic models still significantly limits
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their widespread use by the water companies.
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Note that the aforementioned techniques are based on intermittent pipeline inspections in the field and
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involve manual and resource intensive processes for data collection, transfer to the point of use, and
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analysis. Opposite of that, automatic detection techniques that make use of data from permanently
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installed sensors may provide a more rapid response to the pipe burst events. Negative pressure wave-
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based techniques (e.g., Misiunas et al. 2005; Srirangarajan et al. 2011) belong to this group. The
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sensors required by these techniques, however, are quite expensive. Furthermore, as they record the
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data at very high frequencies, the maintenance and data transmission costs are significant as well.
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These techniques have the same limitations of the transient analysis-based techniques. Additionally,
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they have to cope with the unknown shape of a pipe burst event-induced transient, noise from the
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normal pipeline/pipeline system operations and often very weak pipe burst signatures. All this makes
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these techniques difficult to apply to large pipeline systems with complicated configurations.
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Techniques that attempt to use statistical and AI techniques for automatically processing operational
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variables (e.g., pressure and flow) in near real-time have recently started to appear. This is mainly due
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to the latest developments in hydraulic sensor technology/on-line data acquisition systems, which
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have enabled water companies to deploy a larger number of more accurate and cheaper pressure and
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flow devices. To this group belong techniques such as the hybrid ANN/Fuzzy Inference System
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described in Mounce et al. (2010), the Principal Component Analysis based technique proposed by
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Palau et al. (2011), the Adaptive Kalman Filtering technique proposed by Fenner and Ye (2011), and
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the Support Vector Machines technique proposed by Mounce et al. (2011). These techniques are very
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promising in the context of extracting useful information (required for making reliable operational
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decisions) from the vast amount of and often imperfect sensor data collected by modern Supervisory
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Control And Data Acquisition (SCADA) systems. Statistical/AI-based have a requirement for
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pressure and/or flow measurements sampled much less frequently (e.g., every 15 minutes) than those
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required for transient analysis. Also, pressure and/or flow measurements come from a limited number
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of sensors permanently installed in the pipeline system. Furthermore, these techniques rely on
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empirical observation of the behaviour of the pipeline system, thus precise knowledge of the pipeline
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and instrumentation parameters is not required.
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Despite their initial success, the aforementioned statistical/AI-based techniques can be further
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improved in terms of both detection reliability and detection time. Romano et al. (2012) described the
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development of a methodology for the automated near real-time detection of pipe bursts and other
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events (which induce similar abnormal pressure/flow variations) that offers noticeable improvements
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over the aforementioned statistical/AI-based techniques. They showed that the use of: (i) advanced
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techniques for more efficient and effective processing of the hydraulic data gathered (i.e., wavelets for
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removing noise from the measured flow and especially pressure signals), (ii) different ensembles of
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statistical/AI techniques (i.e., Statistical Process Control, and ANNs) for recognising the various types
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of evidence of a burst/other event occurrence, and (iii) a probabilistic inference engine based on
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Bayesian Networks (Edwards 2000; Jensen 2001) for simultaneously (synergistically) analysing
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multiple evidence/signals at the DMA level, resulted in more reliable and faster detections.
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EVENT RECOGNITION SYSTEM OVERVIEW
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The pressure and flow signals from a DMA show daily, weekly and seasonal variations and are also
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influenced by socioeconomic and meteorological factors such as population characteristics or number
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of industrial establishment and air temperature or precipitation. Furthermore, they show a different
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behaviour under the DMA normal and abnormal (e.g., when a pipe burst has occurred) operating
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conditions. However, their pattern is specific to a particular location. During the DMA normal
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operating conditions, it gives this means that a signal may show a predictable pattern or fingerprint. It
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should be therefore feasible, during the DMA abnormal operating conditions, to identify the pipe
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burst/other event-induced pressure/flow deviations from this predictable pattern fingerprint. Note that
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hereafter event will be used as a generic term to indicate pipe bursts and other events which induce
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similar abnormal pressure/flow variations. The acronym NOP (i.e., Normal Operating Pattern) will be
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used to refer to the pattern of a (pressure or flow) signal assuming that no event occurred in the DMA
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being studied (i.e., during the DMA normal operating conditions).
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In the light on the above assumptions, a computer-based ERS which implements a novel event
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detection methodology has been recently developed (Romano et al. 2012). This section presents a
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brief overview of this system together with relevant details associated with the newly introduced
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Evolutionary Algorithm and Expectation Maximisation based modules which enable implementing
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the novel (re)calibration methodology presented in this paper. A more detailed description of the ERS
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is available in the above reference.
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The data processing route in the ERS starts by receiving the data communicated by the sensors
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deployed in the DMA being studied. For each DMA signal and at each communication interval, u
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readings are obtained (e.g., 2 readings – assuming 15 minute sampled data, which are communicated
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every 30 minutes to improve the sensors’ battery life). These readings update a time series record
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which is stored in a Time Series database. Once all the DMA signals are fully processed as described
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below, the resulting u probability values that an event has occurred in the DMA and any additional
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information that may be used to perform a diagnosis of the event occurring (e.g., to determine the
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likely cause of an alarm) are stored in the Alarms database. If any of the u probability values exceed a
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fixed detection threshold an alarm is generated. In order to avoid raising unnecessary detection alarms
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for the same event at the following communication intervals, however, any further detection alarm is
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suppressed for a user specified ‘alarm inactivity time’ period. Note that the choice of this parameter is
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dependent on the time taken to repair the burst and the pressure/flow variations to go back to normal.
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Figure 1. To appear here.
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Figure 1 shows a diagrammatic representation of the ERS. As it can be observed from this figure, the
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processing of the pressure/flow data is performed into the four ERS components (i.e., dashed dotted
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rectangles) as follows:
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1. Capturing of the NOPs of the various DMA pressure/flow signals;
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2. Identification and estimation of the event-induced deviations between observed (i.e.,
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measured) and captured DMA signal patterns;
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3. Inference about the probability that an event has actually occurred based on above deviations.
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4. (Re)calibration of the probabilistic inference engine based on the information about past
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events occurred in the DMA being studied.
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Note that the first three ERS components are used in a fully automatic fashion for the actual event
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detection. The last ERS component is used in a semi-automatic fashion (i.e., on behest of the user
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when the past events information is available) for the initial calibration and the follow-on periodic
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recalibrations of the DMA level BIS.
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Figure 1 also shows that the aforementioned four ERS components are further organised into six
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subsystems (i.e., solid snipped corner rectangles) each containing a number of different modules (i.e.,
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solid rectangles). The six ERS subsystems are as follows: (1) the Setup subsystem, (2) the
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Discrepancy Based Analysis (DBA) subsystem, (3) the Boundary Based Analysis (BBA) subsystem,
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(4) the Trend Based Analysis (TBA) subsystem, (5) the Inference subsystem, and (6) the Bayesian
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Inference System (BIS) parameters learning subsystem.
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The first ERS subsystem (equivalent to the first ERS component) is used to perform the pressure/flow
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signal NOP capturing. Its first two modules (i.e., data retrieval, and data pre-processing) are used for
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retrieving the historical data from the Time Series database and assembling a set of data that best
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represents the most recent NOP of the DMA signal being analysed (i.e., NOP data set). Once this is
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done, the third module (i.e., statistics estimation) is used for estimating several vectors of descriptive
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statistics from the NOP data set. The remaining modules (i.e., the data de-noising module, the newly
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introduced ANN parameters & input structure selection module, and the ANN training & testing
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module), on the other hand, are first used for removing noise from the NOP data set and then for: (i)
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automatically selecting the optimal (i.e., that yield the best forecasting performance) ANN input
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structure and parameters set (by means of an Evolutionary Algorithm optimisation strategy), (ii)
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training and testing a “specialised” (i.e., signal-specific) ANN prediction model (by using the
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optimised ANN input structure and parameters set), and (iii) estimating the ANN model prediction
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error’s variability.
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The second, third and fourth ERS subsystems are used synergistically to perform the deviations
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identification and estimation data analysis in the second ERS component. This is done as follows: (i)
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the DBA subsystem checks that the discrepancies between the incoming observed DMA signal values
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and their ANN predicted counterparts do not exceed pre-defined limits based on the estimated ANN
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model prediction error’s variability, (ii) the BBA subsystem checks that the incoming observed DMA
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signal values lie inside a “data envelope” whose boundaries are defined by using the vectors of
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descriptive statistics estimated from the NOP data set, and (iii) the TBA subsystem monitors, on a
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Control Chart (Shewhart 1931), how the mean of the historical DMA signal values recorded during a
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particular time window during the day (e.g., from midnight to 4 am, 4am to 8 am, etc.) varies over
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time. The reason for using three subsystems is that, by using an ensemble of different statistical and
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AI techniques, each of them focuses on recognising a specific type of evidence that an event has
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occurred. Furthermore, since they perform tasks in parallel they allow simultaneously assessing how
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an event affects the pressure/flow measurements from different perspectives (e.g., short-term and
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long-term effects).
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The fifth ERS subsystem (equivalent to the third ERS component) is used to perform the event
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probability inference data analysis. Starting from the event occurrence evidence generated as
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described above, BISs are used here for: (i) combining the generated event occurrence evidence, (ii)
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inferring the probability of an event occurrence in the DMA, (iii) raising detection alarms, and (iv)
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providinge additional information for incident diagnosis.
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Finally, the newly introduced sixth ERS subsystem, namely the BIS parameters learning subsystem
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(equivalent to the fourth ERS component), is used to perform the inference engine (re)calibration data
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analysis. The main aim is to improve the classification performance of the DMA level BIS and hence
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the detection performance of the ERS. As it will be shown in the relevant section, this is achieved by
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using: (i) an Expectation Maximisation strategy, and (ii) information (i.e., start time and duration)
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about the past events occurred in the DMA being studied (e.g., obtained from the water company’s
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historical records and/or from periodic reviews of the alarms raised by the ERS). The data analyses
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carried out in this subsystem are organised into the following two modules: (1) data retrieval module,
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and (2) Expectation Maximisation (EM) based parameters learning module. The first module is used
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for retrieving the past events information (assuming that it has been obtained and stored in the Alarms
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database). This information forms the data set of ‘event cases’ which is then used in the second
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module for (re)calibrating the parameters of the DMA level BIS. Once this is done, the (re)calibrated
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parameters are passed on to the Inference subsystem for use in the DMA level BIS.
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As it is shown in Figure 1, the ERS has three main modes of operation: (1) the “Assemble” mode, (2)
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the “Execute” mode, and (3) the “Learn” mode. These modes of operation define the time schedule
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according to which the data analyses in each subsystem are performed. The “Assemble” mode is used
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for ‘tuning’ the data-driven ERS when it is initialised (i.e., used for the first time in a DMA). Later on,
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it is used: (i) regularly (i.e., every l days - e.g., every week) when the ERS is updated (to capture the
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latest normal operating conditions of a DMA) thereby providing a continuously adaptive ERS, and (ii)
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periodically (i.e., every h days - e.g., every three months) when the ERS is reinitialised (to account for
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the seasonal variations in the DMA’s pressure/flow regime, growing demand over time, etc.; or
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following occasional operational/other DMA changes - e.g., re-valving). The “Execute” mode is the
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normal operating mode used at every communication interval to detect the events and raise the
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alarms. Finally, the “Learn” mode may be used for the initial calibration and for the follow-on
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periodic recalibrations of the ERS probabilistic inference engine. As the data analyses performed in
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this mode of operation have a requirement for the past events information, however, its actual
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utilization depends on whether or not this information is available/considered.
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OPTIMISATION OF ARTIFICIAL NEURAL NETWORK PARAMETERS AND
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INPUT STRUCTURE OPTIMISATION
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An ANN model is used in the ERS for performing short-term prediction (i.e., one time step ahead) of
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the future values of the particular DMA signal being analysed. The reason for choosing an ANN
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model is the inherent complexity of the WDSs. The main aim is to exploit the ability of this powerful
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data modelling tool to model any function without explicit knowledge of the parameters involved.
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This said and despite the fact that the efficiency and superiority of the ANN models over approaches
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that employ time-series analysis, regression models, and Autoregressive Integrated Moving Average
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models for in modelling and forecasting water consumption has been demonstrated in a large number
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of studies (e.g., Adamowski 2008), several issues have to be considered in order to build ANN models
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that exhibit good forecasting performance for different DMA signals. These issues include the choice
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of the ANN input structures, and of the ANN parameters.
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Figure 2. To appear here.
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Generally speaking, as in the ERS presented in Romano et al. (2012), a suitable ANN input structure
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for solving the problem at hand would include a certain number of past pressure/flow values (i.e.,
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LagSize), and other explanatory variables such as the Time of the Day (TofD) (i.e., a value between 1
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and g, where 1 corresponds to midnight and g is the number of samples in one day) and the Day of the
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Week (DofW) (i.e., a value between 1 and 7) associated with the forecasting horizon (i.e., next time
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step) (which have to be converted into a field type form to avoid data representation issues when
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using ANN models). This is shown in Figure 2. Note that in this framework a field type form (i.e.,
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ones and zeros) has to be used for encoding the TofD and DofW indices. This is motivated by data
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representation issues when using ANN models. These indices, in fact, can be seen as a finite set of
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categorical data. Despite they have a natural ordering (e.g., Tuesday follows Monday), they do not
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have an intrinsic ‘value’ associated with them (e.g., Tuesday is more important than Monday). Thus to
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prevent the ANN model from learning these artificial relationships a ‘binary’ flag has to be created for
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each possible value (e.g., Monday-flag=0000001, Tuesday-flag=0000010, etc.). A strategy for
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selecting suitable ANN parameters (that enables striking a balance between learning and
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generalization), on the other hand, would involve (e.g., Nelson and Illingworth 1991; Moody 1992):
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(i) choosing a sufficiently large number of hidden neurons (to ensure the ANN model is flexible), and
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(ii) controlling the number of training cycles and/or applying a penalisation coefficient  (i.e.,
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coefficient of Weight Decay Regularisation - Bishop 1995) to the weights of the ANN model (to
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control the flexibility of the ANN model).
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With a view to the application of the ERS to entire WDSs, however, the use of the same LagSize,
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explanatory variables, number of hidden neurons, number of training cycles, and coefficient of
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Weight Decay Regularisation for all the analysed DMA signals (i.e., a pre-defined ANN input
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structure and parameters set) has the potential to lead to the development of ANN prediction models
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that exhibit sub-optimal forecasting performance. This is because signals from different DMA types
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(e.g., rural, residential, etc.) and different DMA signal types (e.g., pressure vs. flow) may show
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extremely varying patterns.
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Bearing in mind the above, the objective of the new methodology presented here is as follows. For
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each analysed DMA signal, to select the ANN input structure and parameters set that enables the
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resulting ANN prediction model to yield the best forecasting performance. This said, it is important to
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stress that the potential benefits resulting from doing this are two-fold. On the one hand, the quality of
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the ANN models’ predictions improves. On the other hand, as the resulting ANN models are signal-
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specific, the ERS becomes “tailored” to the particular DMA to which it is applied, whilst more
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generally applicable to different DMAs.
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It is clear, however, that the selection of the optimal input structure and parameters set for each ANN
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model is a combinatorial problem. In this scenario and bearing in mind that the ERS has to potentially
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deal with many hundreds of different signals, the use of a manual trial and error procedure would not
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be feasible. Similarly, the use of an automated full enumeration procedure would be far too
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computational expensive. Therefore, an Evolutionary Algorithm optimisation strategy is brought into
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play here. The main reason for this is that Evolutionary Algorithms do well in large search spaces by
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working only with a sample available population and have the power to discover good solutions
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rapidly for difficult high-dimensional problems. Thus, they enable circumventing the computational
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limitations of the “brute-force” methods that use full search space enumeration.
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The term Evolutionary Algorithm is used for a broad spectrum of heuristic approaches that simulate
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evolution. Primary examples include Genetic Algorithms (Holland 1975), and Evolutionary Strategies
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(Schwefel 1981). Because of their relative efficiency, Evolutionary Algorithms have been extensively
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applied in the water resources planning and management field to solve a wide range of problems (see
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Nicklow et al. 2010). These include (similarly to what presented in this paper) the optimal ‘design’ of
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ANN prediction models (e.g., Giustolisi and Simeone 2006).
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Considering the ANN parameters and the variables that define the ANN input structure shown in
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Table 1 as the set of decision variables (i.e., design parameters) for the problem at hand, the
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Evolutionary Strategy described in Schwefel (1981) is used here for automatically finding the set of
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decision variables that minimises the ANN model prediction error on the test set (i.e., a randomly
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chosen subset - e.g., 30% - of the de-noised NOP data set). The ANN model prediction error on the
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test set is computed by using the Nash-Sutcliffe index (Nash and Sutcliffe 1970). Note that the range
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of values used in optimisation for the ANN parameters and the variables that define the ANN input
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structure shown in Table 1 were selected after carrying out a number of preliminary tests aimed at
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defining the size of the search space that is likely to enable finding an optimal solution for the
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problem at hand.
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Table 1. To appear here.
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As it is shown in Figure 1, the above optimised set of decision variables is then passed on to the ANN
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training & testing module where it is used to build the signal-specific ANN prediction model. This
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said, note that in Figure 1 it is also shown that the ANN parameters & input structure selection
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module is not used when the ERS is updated. The ANN parameters and input structure selected at
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ERS (re)initialisation continue to be used at each ERS updating time. The rationale is that only
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relatively minor changes are expected to affect the NOP of a DMA signal in the interval between two
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updates. Thus, in principle, the possible decline in the ANN forecasting performance does not justify
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the added computational burden of using the Evolutionary Algorithm optimisation strategy.
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BAYESIAN INFERENCE SYSTEM (RE)CALIBRATION
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Various (i.e., one for each DMA signal) Signal level BISs and one DMA level BIS are used in the
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ERS for inferring, at each time step during a data communication interval, the probability that an
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event has occurred in the DMA being studied. Each of these BISs consists of a Bayesian Network
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(Edwards 2000; Jensen 2001). This Bayesian Network combines all the evidence of an event
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occurrence resulting from the three ERS analysis subsystems and, in the case of the DMA level BIS
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only, coming simultaneously from all the DMA signals (see Figure 1). Bayesian Networks are used
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here because they allow reasoning under uncertainty and updating the probability that an event has
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occurred as evidence accumulates. With enough evidence, it should become very high or very low.
334
A Bayesian Network is a directed graph consisting of nodes and arcs. Each node represents a random
335
variable or a group of random variables whilst the arcs express a probabilistic relationship between
336
these variables. A Conditional Probability Table (CPT) is associated with each node. The CPTs
337
contain the prior probabilities of all root nodes (i.e., nodes with no predecessors) and the conditional
338
probabilities of all non root nodes given all the possible combinations of their direct predecessors.
339
These prior/conditional probabilities encode the strengths of the dependencies among the nodes.
340
According to Jensen (2009), there are two knowledge sources for selecting the parameters (i.e.,
341
prior/conditional probabilities) in the CPTs of a Bayesian Network. These are: (i) domain experts, and
342
(ii) databases.
343
The CPT parameters ‘normally’ used (i.e., when no information about past events is
344
available/considered) by the ERS in its Signal and DMA level BISs are the same for each signal and
345
for every DMA. The CPT parameters ‘normally’ used by the ERS in its DMA level BIS are the same
346
for every DMA. These CPT parameters have been selected according to the former knowledge source
347
(i.e., domain experts). Specifically, this has been done by carrying out a number of preliminary tests
348
(results not shown here) and by incorporating domain knowledge obtained by the theoretical research
10
349
framework, literature, and observational experience. An example of these parameters is given in
350
Figure 3.
351
Figure 3. To appear here.
352
Alternatively, when information about past events is available, the CPT parameters could be
353
(re)calibrated directly from these data (i.e., ‘event cases’). Note that this is commonly known as the
354
Bayesian Network parameters learning problem (Heckerman 1995). In this scenario, if the structures
355
of a Bayesian Network (or equivalently BIS) has no hidden nodes (i.e., those for which there is no
356
observed data), the estimation of the parameters is simple and can be done just by calculating
357
(counting and dividing) the prior or conditional probabilities. As the BISs used in the ERS include
358
such nodes (see for example the ‘alert’ nodes in Figure 3), however, they are only partially
359
observable. Therefore, an algorithm capable of estimating the CPT parameters from incomplete data
360
must be used.
361
The Expectation Maximisation algorithm (Dempster et al. 1977; Lauritzen 1995) is the most
362
commonly employed algorithm for estimating CPT parameters from incomplete data (Jensen 2009).
363
In theory, other numerical optimization techniques, such as Gradient Descent or Newton-Raphson,
364
could be used instead of Expectation Maximisation. In practice, however, the Expectation
365
Maximisation algorithm has the advantage of being simple, robust and easy to implement (Do and
366
Batzoglou 2008). This algorithm was developed in the statistics community by Dempster et al. (1977)
367
and adapted for use with the Bayesian Networks by Lauritzen (1995). The Expectation Maximisation
368
is an algorithm that, given a set of training data, determines estimates of the CPT parameters that are
369
optimal within a neighbouring set of solutions. It starts with initial values (e.g., chosen at random) for
370
all the parameters in the CPTs of a Bayesian Network, and then iteratively refines them. Each
371
iteration ensures that the likelihood function increases and eventually converges to a local maximum.
372
The iteration process consists of two steps, namely the Expectation and Maximisation steps, which are
373
performed in alternating manner until convergence.
374
In the light of the above, it is important to note that both the CPT parameters of the various Signal
375
level BISs and the CPT parameters of the DMA level BIS could be (re)calibrated by using
376
information about the confirmed past events. However, in the ERS such information is used for
377
(re)calibrating the CPT parameters of the DMA level BIS only. This is because, in the ERS, only the
378
DMA level BIS is used for raising the detection alarms. Furthermore, as a particular past event may
379
have occurred anywhere in the DMA, it may have not affected the measurements from a sensor
380
located farther away from it. In this scenario, “forcing” changes (through learning) to the CPT
11
381
parameters of that sensor’s Signal level BIS(s) in order to obtain high Signal level event occurrence
382
probabilities could be counterproductive.
383
CASE STUDY
384
Description
385
In this section Tthe data analyses performed to evaluate the benefits of the Evolutionary Algorithm
386
and Expectation Maximisation optimisation strategies are presented here. In order to evaluate the
387
benefits of the Evolutionary Algorithm strategy for selecting optimal ANN input structure and
388
parameters sets, the ERS was tested and verified on real-life events. In order to evaluate the benefits
389
of the Expectation Maximisation strategy for (re)calibrating the parameters in the CPTs of the DMA
390
level BIS, the ERS was tested and verified: (i) on a series of Engineered Events (EEs), whereby fire
391
hydrants were opened to simulate different pipe burst events, and (ii) on synthetic pipe burst events
392
whereby fictitious “burst flows” were arbitrarily added to an actual flow signal.
393
In the first case, the data analyses performed made use of the pressure and flow data recorded by the
394
sensors deployed in five UK DMAs during the eleven month period from July 2009 to June 2010.The
395
evaluation of the Evolutionary Algorithm strategy’s benefits was carried out as follows. Five UK
396
DMAs were selected. These selected DMAs have different characteristics and varying sizes. As an
397
ensemble, in fact, they contain light industrial, urban, semi rural, and rural areas. The number of
398
domestic properties in each of them varies between 409 and 3,493. The number of commercial users
399
varies between 11 and 231. Their individual total mains length varies between 6.3 and 30 km. These
400
DMAs are equipped with a flow sensor at the DMA inlet and a pressure sensor at the critical point
401
(i.e., the one located either at the point of highest elevation or alternatively at a location farthest away
402
from the inlet) in the DMA and, in one case only, with a flow and pressure sensor at the DMA inlet
403
only. The pressure and flow data recorded by all these sensors during the eleven month period from
404
July 2009 to June 2010 were used. This said, it has to be stressed that, although the ERS
405
simultaneously processes the data coming from the relevant pressure/flow sensors deployed in a
406
single DMA to raise detection alarms for that particular DMA (i.e., the ERS is applied to each DMA
407
independently), the results of data analyses aimed at evaluating the Evolutionary Algorithm strategy’s
408
benefits will be presented in the ANN optimisation results section in an aggregated form (i.e., results
409
for all the five selected DMAs).
410
In the second case, the data analyses performed when the ERS was tested and verified on the EEs
411
made use of the pressure and flow data recorded by the sensors deployed in a sixth UK DMA during
412
July-August 2009 and March 2010 (as the EEs were conducted in these 3 months). The evaluation of
12
413
the Expectation Maximisation strategy’s benefits was carried out as follows. On the one hand, a sixth
414
UK DMA was considered when the ERS was tested and verified on the EEs. This DMA is
415
predominantly urban, it has a total of 2,640 domestic properties and 500 commercial users. The total
416
mains length is 24 km. It is equipped with a pressure and flow sensor at the DMA inlet as well as one
417
pressure sensor at the critical DMA point. The pressure and flow data recorded by all these sensors
418
during July-August 2009 and March 2010 (as the EEs were conducted in these 3 months) were used
419
for raising detection alarms for this particular DMA. On the other hand, a seventh UK DMA was
420
considered when the ERS was tested and verified on the synthetic pipe burst events. This DMA is also
421
predominantly urban, it has a total of 1,916 domestic properties and 234 commercial users. The total
422
mains length is about 27 km. This DMA is equipped with eight pressure sensors within the DMA and
423
two flow sensors at the DMA inlets. However, only the data recorded during February-March 2012 by
424
the flow sensor deployed at one of the DMA inlets were used for raising detection alarms for this
425
particular DMA.
426
In both cases the aforementioned evaluations, the considered DMAs are gravity fed and have no
427
storage. tThe sensors recorded data at 15 minute intervals. The flow data were averaged values during
428
the 15 minute sampling interval whilst the pressure data were 15 minute instantaneous values. Note
429
that although historical data were used for the data analyses performed here, the pressure and/or flow
430
measurements were fed to the ERS in a simulated ‘on-line’ fashion (i.e., as the ERS would have been
431
used in real-life). The user-defined ERS parameters used for the case study analyses are as in Romano
432
et al. (2012). The ERS was not reinitialised.
433
Artificial Neural Network Optimisation Results
434
In order to evaluate the benefits of the Evolutionary Algorithm optimisation strategy, the ERS was
435
tested with and without making use of the ANN parameters & input structure selection module (see
436
Figure 1). When this module was not used, the ANN parameters and input structure employed for all
437
the ANN models (i.e., all the signals coming from the DMAs being studied) were the same and
438
chosen as follows. The number of hidden neurons was computed by using the Neuroshell2
439
(Neuroshell2 manual 1996) rule of thumb. The coefficient of Weight Decay Regularisation was
440
chosen as equal to 0.01. The number of training cycles was chosen as equal to 400. The ANN input
441
structure included 4 past pressure/flow values, and the TofD and DofW explanatory variables. Note
442
that the use of these particular ANN parameters and input structure was found, after a number of
443
preliminary tests, to ensure that the resulting ANN prediction models were able to closely
444
approximate the training sets whilst allowing good generalisation performance for all the considered
445
signals.
13
446
In the data analyses performed here, the value of the ‘alarm inactivity time’ parameter was set as
447
equal to 1 week. With this setting, when the Evolutionary Algorithm optimisation strategy was used,
448
the ERS raised a total of 37 alarms. In the opposite case (i.e., the Evolutionary Algorithm optimisation
449
strategy was not used), it raised a total of 38 alarms. In both cases, the raised alarms were later
450
compared against a set of events identified by means of a careful visual inspection of the signal trends
451
supported by data on Main Repair (MR) works carried out in the network and on recorded Customer
452
Contacts (CCs) (i.e., customer complaints about potential problems related to water supply). This set
453
of events included: (i) 17 burst events (i.e., related to the MR records), (ii) 7 pressure/flow anomalies
454
whose exact cause is uncertain (e.g., illegal water usage, unusual system activity, operational DMA
455
changes, etc.) but for which a record existed (i.e., CC records), (iii) 1 sensor failure event, and (iv) 5
456
other visible pressure/flow anomalies which were, however, not accompanied by any CC or MR
457
records (i.e., did not impact the customers). Note that further information about the performed visual
458
inspection of the signal trends can be found in Romano et al. (2012). The aforementioned comparison
459
enabled to check if a correlation existed (i.e., genuine alarms) or not (i.e., false alarms) and, in turn, to
460
evaluate the ERS performance (i.e., success rate, and reliability).
461
In the case of ANN optimisation, of the 37 raised alarms: (i) 21 alarms were correlated to the 17 burst
462
events, (ii) 7 alarms were correlated to the 7 pressure/flow anomalies that generated several CCs, (iii)
463
3 alarms were correlated to the sensor failure event, (iv) 5 alarms were correlated to the 5 visible
464
pressure/flow anomalies that did not affect the customers, and (v) 1 was a false alarms. On the other
465
hand, when the ANN optimisation was not carried out, of the 38 raised alarms: (i) 21 alarms were
466
correlated to the 17 burst events, (ii) 6 alarms were correlated to the pressure/flow anomalies that
467
generated several CCs, (iii) 3 alarms were correlated to the sensor failure event, (iv) 5 alarms were
468
correlated to the 5 visible pressure/flow anomalies that did not affect the customers, and (v) 3 were
469
false alarms. Note that because of the ‘alarm inactivity time’ parameter used, multiple alarms were
470
sometime related to the same events. Furthermore, some events caused alarms in different DMAs.
471
Figure 4 summarises the above results. In the light of the results obtained, it is possible to state that
472
the use of the Evolutionary Algorithm optimisation strategy improved both the ERS event detection
473
reliability and effectiveness. In fact, the number of false alarms was reduced three-fold (from 3 to 1),
474
and one additional event that resulted in several CCs being received was detected.
475
Figure 4. To appear here.
476
The improved event detection reliability and efficiency obtained in this case study, however, are not
477
the only benefits yielded by the use of the Evolutionary Algorithm optimisation strategy. In fact, the
478
ERS detection speed was also enhanced. As an example, Figure 5 shows the results obtained when a
14
479
large (i.e., about 30 l/s) burst event occurred. Six CCs (shown as vertical lines with a circle) and one
480
MR (not shown as it did not have an associated time) were recorded during this event. When the ANN
481
optimisation was used, the ERS raised an alarm 30 minutes before the first CC was received. On the
482
other hand, when it was not used, the ERS raised an alarm 45 minutes later. That is to say, 15 minutes
483
after the first CC. The fact that by making use of the Evolutionary Algorithm optimisation strategy the
484
ERS could have detected this burst event ahead of the customers is very important. This is because the
485
early information may have enabled the water company to react more quickly and decrease the
486
potential damages to the infrastructures and to third parties. Furthermore, it may have also helped the
487
company to improve its customer service by: (i) reducing the time of the supply interruption, (ii)
488
enabling to allocate more time for planning and implementing mitigation measures (if the supply
489
interruption could have not been avoided), and (iii) allowing proactive and/or more informed
490
communications with the customers.
491
Figure 5. To appear here.
492
Bayesian Inference System C(Re)calibration Results
493
Tests on Engineered Events
494
In the data analyses performed here order to evaluate the benefits of the Expectation Maximisation
495
strategy, the capabilities of the ERS with the parameters in the CPTs of the DMA level BIS based on
496
domain experts knowledge were compared with those of the ERS with the parameters in the CPTs of
497
the DMA level BIS calibrated by using information about some of the EEs carried out. Here, the ERS
498
capabilities were evaluated based on comparisons between the ERS detection times for the two
499
relevant cases considered and the corresponding actual hydrant opening times. In addition to this, the
500
Receiver Operating Characteristics (ROC) graphs (Egan 1975) were used too. Note that a ROC graph
501
is a technique for visualizing and selecting classifiers based on their performance. ROC graphs have
502
long been used in signal detection theory to depict the trade-off between true and false alarm rates of
503
classifiers.
504
A total of 9 EEs were carried out as follows: 3 in July 2009, 3 in August 2009, and 3 in March 2010.
505
For the purposes of the analysis that evaluated the ERS capabilities based on comparisons between the
506
ERS detection times and the corresponding actual hydrant opening times, the CPT parameters were
507
calibrated by making use of the information about the start and end times of the 6 EEs carried out in
508
July 2009 and August 2009. Note that, in this analysis, the ‘alarm inactivity time’ parameter was set
509
as equal to 1 day. This is because any single EE lasted one day maximum and different EEs were
510
sometimes carried out during the same week.
15
511
Table 2 shows the ERS detection times obtained for the two relevant cases considered and the
512
corresponding actual hydrant opening and closing times for all the EEs. The underlined alarm start
513
times refer to those events that were detected at the best possible time (within the 15-minute sampling
514
rate). Alarm start times in normal text font refer to those events that were detected with a delay not
515
greater than one hour, whilst alarm start times in bold refer to those events that were detected with
516
delays longer than 1 hour.
517
As it can be seen from Table 2, in both cases all the EEs were successfully detected. However, when
518
the calibration procedure was used, the detection speed improved significantly. Given that the CPT
519
parameters were calibrated by using the July-August 2009 EEs’ start and end times information, it is
520
not unexpected that the EEs carried out during these two months were timely detected (i.e., EE3 with
521
a 15 minute delay only, and the other EEs at the best possible time). This said, the significant
522
detection speed improvement is evident when the EEs carried out in March 2009 2010 are considered
523
(i.e., set of EEs not used for calibration). The first of these EEs, in fact, was detected 11 hours and 30
524
minutes earlier than in the case where the calibration procedure was not used. Additionally, the third
525
of these EEs was detected 15 minutes earlier (resulting in detecting it at the best possible time).
526
Finally, a “detection speed improvement” can also be observed for the second of the March 2009
527
2010 EEs. The additional time gained would have made a lot of difference in real-life in terms of
528
repairing the pipe burst and reducing the negative impact on the nearby customers.
529
With regard to the second of the March 2009 2010 EEs, however, the following consideration applies
530
to both cases studied. The close proximity in time between EEs (i.e., 10 minutes separated the first
531
and the second EEs carried out in March 2009 2010) together with the chosen value for the ‘alarm
532
inactivity time’ parameter, made possible to raise the relevant alarm only 1 day after the alarm for the
533
first EE was raised. Bearing in mind this fact, on the 2nd of March 2010 at 08:00 the ERS generated a
534
detection probability of 0.68 and 0.74 in the case of CPT parameters based on domain experts
535
knowledge and calibrated by using the EEs information, respectively. As both generated detection
536
probabilities were above the 0.5 user-defined detection threshold for raising the alarms, the ERS
537
would have raised an alarm for that particular EE at the best possible time if it had not been carried
538
out the day immediately after the first EE.
539
Table 2. To appear here.
540
The above analysis shows that the Expectation Maximisation strategy is beneficial for improving the
541
detection speed of the ERS. That analysis alone, however, does not allow conclusions making
542
conclusion about the calibrated DMA level BIS superiority to be made. Therefore, ROC graphs were
16
543
used in the analysis carried out as shown below in order compare the classification performance of the
544
DMA level BIS with CPT parameters based on domain experts knowledge with those that of the
545
DMA level BISs with CPT parameters calibrated by using the EEs information.
546
In this analysis, the value of the ‘alarm inactivity time’ parameter was set as equal to 15 minutes (i.e.,
547
all the DMA level event occurrence probabilities greater than the detection threshold raised detection
548
alarms). This is because the ROC graph’s true and false alarm rates are obtained by comparison, at
549
every time step, between the status of a hydrant (i.e., opened/closed) and the output of the relevant
550
DMA level BIS (i.e., DMA level event occurrence probability greater/smaller than the detection
551
threshold). Additionally, given the limited availability of “event cases”, a four step procedure
552
involving the use of a cross-validation technique was used. The first step of this procedure involved,
553
separately evaluating the classification performances of the DMA level BIS with the CPT parameters
554
based on domain experts knowledge on each of the three months studied. The second step involved
555
calibrating the CPT parameters by using, in turn, information about the EEs carried out during two of
556
the three months considered (i.e., August 2009 and March 2010, July 2009 and March 2010, and July
557
2009 and August 2009) and evaluating the resulting DMA level BIS classification performance on the
558
remaining month (i.e., July 2009, August 2009, and March 2010). As a result of these first two steps,
559
6 ROC curves representing the classification performances of the relevant DMA level BISs were
560
obtained (i.e., 1 for each month and for each relevant case considered). The third step involved using
561
the Vertical Averaging technique (Fawcett 2006) for averaging the 3 ROC curves obtained for each of
562
the two relevant cases considered. Finally, a measure of variance was derived for visualising the
563
classification performance variability across the three months studied (i.e., 3-fold cross-validation
564
runs).
565
Figure 6 shows the results obtained after applying the above procedure. The two ROC curves
566
represent the ‘average’ classification performance (across the three months studied) of the relevant
567
DMA level BISs for the two cases considered. The Box plots show the classification performance
568
variability. It is possible to observe from this figure that performance is similar for low false positive
569
rates (i.e., 0.05). That is, in both cases, reliable positive classifications (i.e., event occurrence) are
570
made with strong evidence. However, for higher false positive rates the DMA level BISs with
571
calibrated CPT parameters perform better than the DMA level BIS with CPT parameters based on
572
domain experts knowledge and also show less variability. The results of this analysis show clearly
573
that the detection reliability and effectiveness of the ERS can be improved if information about past
574
events is used for calibrating the parameters in the CPTs of the DMA level BIS.
575
Figure 6. To appear here.
17
576
Tests on synthetic pipe burst events
577
A cross-validation technique was used in the analysis performed as outlined above. However, it is
578
important to stress that when the ERS is used for the on-line monitoring of a DMA, the past events
579
information could be more efficiently exploited by using a procedure that enables the semi-automatic
580
(re)calibration of the CPT parameters as knowledge about the events occurred in the DMA being
581
monitored becomes available. This said the following ‘cumulative learning’ procedure is proposed
582
here. Once information about a certain number of ‘event cases’ become available for the first time, it
583
is used for calibrating the CPT parameters. Subsequently, when information about new ‘event cases’
584
become available, it is used together with (‘cumulative learning’) the previously used information for
585
recalibrating the CPT parameters.
586
To this end, it is also important to note that the past events information is very difficult to obtain if the
587
current water company’s historical records are used (because of the nature of underground pipe bursts
588
and due to the fact that the MR and CC records do not provide reliable information about the exact
589
start date/time and duration of these events). However, when the ERS is used for the on-line
590
monitoring of a DMA, the past events information could be more easily obtained by performing
591
periodic reviews of the alarms raised by the ERS. Indeed, assuming that the ERS alarms are timely,
592
such reviews have the potential to enable an operator to simply flag the genuine alarms (which have
593
an associated alarm start time) as confirmed and check the associated event durations. In this way,
594
Progressing in a like fashion, over time, the Alarms database will be populated with ‘cases’ of events
595
of different type and size that occurred in different areas of the DMA being monitored. In this
596
scenario, this the use of the ‘cumulative learning’ procedure outlined above has the potential of
597
enabling the ERS to learn recognising the features of a large variety of events, thereby continuously
598
improving its generalisation and detection capabilities.
599
In view of the above, the main objective of the data analyses performed here was to demonstrate the
600
benefit of the proposed ‘cumulative learning’ procedure. This was achieved by testing the ERS on a
601
series of synthetic pipe burst events. As shown in Tables 3 and 4, 56 synthetic pipe burst events
602
occurring at different times during the day and with variable durations were simulated by adding
603
fictitious “burst flows” (from 1 to 70 l/s) to the flow time series recorded during the period from the
604
1st of February 2012 to the 31st of March 2012. This resulted in a ‘modified flow time series’. Next,
605
the data in the ‘modified flow time series’ referring to the period from the 1 st of February 2012 to the
606
15th of February 2012 were used to initialise the data driven ERS. Note that this time interval included
607
a total of 10 synthetic pipe burst events which only served the purpose of simulating the presence of
608
abnormal measurements in the raw data that have to be used for the ERS initialisation. Once this was
18
609
done, the ERS detection results obtained during the period between the 1st and the 31st of March
610
(which included a total of 28 synthetic pipe burst events) were evaluated for the following three cases:
611
(1) ERS with the parameters in the CPTs of the DMA level BIS based on domain experts knowledge,
612
(2) ERS with the parameters in the CPTs of the DMA level BIS calibrated by using information about
613
the 9 synthetic pipe burst events simulated during the period between the 15th and the 21st of February
614
2012, and (3) ERS with the parameters in the CPTs of the DMA level BIS recalibrated by using
615
information about the 9 synthetic pipe burst events simulated during the period between the 15th and
616
the 21st of February 2012 and the 9 synthetic pipe burst events simulated during the period between
617
the 22nd and the 29th of February 2012 together.
618
The detection results obtained for each of the aforementioned cases are reported in the last three
619
columns of Table 4. It can be observed that, by calibrating the CPTs of the DMA level BIS using
620
information about the 9 synthetic pipe burst events simulated during the period between the 15th and
621
the 21st of February 2012, the number of synthetic events that were not detected by the ERS decreased
622
from 11 to 7. Additionally, when the CPTs of the DMA level BIS were recalibrated by using
623
information about the 9 synthetic pipe burst events simulated during the period between the 15th and
624
the 21st of February 2012 and the 9 synthetic pipe burst events simulated during the period between
625
the 22nd and the 29th of February 2012 together, the number of events that were not detected by the
626
ERS was further reduced to 3. This said, it has to be also stressed that in all the three cases considered
627
no false positive alarms were raised. All this demonstrate how the use of the ‘cumulative learning’
628
procedure improves the ERS detection capabilities.
629
Figure 7 shows an example of the result obtained from the ERS tests on the synthetic pipe burst. The
630
figure is divided into two parts. The top part shows the result obtained when domain experts
631
knowledge based CPT parameters were used. The bottom part shows the result obtained when
632
recalibrated parameters were used. In each part of the figure, 6 synthetic events are shown together
633
with the resulting DMA level event occurrence probabilities – i.e., Pglobal - (only if greater than the 0.5
634
detection threshold used for raising alarms) at every time step (every 15 minutes). From this figure, it
635
can be observed that, when the ‘cumulative learning’ procedure was used, not only more events were
636
detected (6 rather than 3) but also some of the events were detected in a more timely manner.
637
CONCLUSIONS
638
An automated methodology for the near real-time detection of pipe bursts and other events at the
639
DMA level from observed pressure/flow signals has been developed recently (Romano et al. 2012).
640
This methodology is implemented in a computer-based ERS which is readily transferable to practice.
19
641
To enable the data-driven (re)calibration of the ERS and to enhance the ERS detection performance,
642
an Evolutionary Algorithm optimisation strategy for automatically selecting the parameters and input
643
structures of the ANN pressure/flow signal prediction models, and an Expectation Maximisation
644
strategy for semi-automatically (re)calibrating the parameters in the CPTs of the DMA level BIS have
645
been developed, presented and tested here.
646
The developed data-driven (re)calibration methodology further extends the self-learning capabilities
647
of the ERS and its ability to work in an online-context. Not only is the ERS able to adapt to changes
648
in the DMA operating conditions but also to evolve as knowledge about past events in the DMA is
649
acquired. Furthermore, by automatically developing ANN models that are signal-specific, the ERS is
650
able to tailor itself to the particular DMA being monitored. All of the above also makes the ERS more
651
generically applicable to different DMAs.
652
The tests performed here to evaluate the performance of the new (re)calibration methodology have
653
involved both real-life pipe burst/other events, and simulated and synthetic pipe burst events in
654
several real-life UK DMAs. The ERS was used with pressure and flow measurements fed in an “on-
655
line” fashion (i.e. as it would have been used in real-life). Two Several sets of ERS runs were
656
performed: with and without making use of the Evolutionary Algorithm and Expectation
657
Maximisation optimisation strategies. The results obtained have shown that the use of these strategies
658
improved the overall ERS performance in terms of event detection reliability and speed. Reliable and
659
timely detections may enable the water companies to gain confidence in the raised alarms and, in turn,
660
minimise the negative impacts of burst/other events therefore improving the water companies’
661
operational efficiency and customer service.
662
Note that the ERS and the novel (re)calibration methodology presented in this paper have been tested
663
and verified, so far, on UK DMAs only. This said, their application to pipe networks in other
664
countries (where DMAs may not have been established) would require further tests.
665
The future work will involve on-line testing of the ERS on a much larger number of DMAs. The aim
666
is to gather further evidence of the benefits yielded by the data-driven (re)calibration methodology
667
presented here and their actual extent. Particular attention will be paid to the task of verifying that the
668
proposed “cumulative learning” procedure leads to continuous improvements of the ERS detection
669
performance. On the other hand, bearing in mind that the water companies are starting to recognise
670
that the near real-time monitoring of their WDSs by means of pressure and flow devices not only
671
provides a potentially useful source of information for quickly and economically detecting the pipe
672
burst events but also yields several other important benefits (e.g., improved network visibility and
20
673
management, higher compliance with regulatory targets, etc.), an increase in the density of coverage
674
of monitoring locations is expected in the near future. In this scenario future work will involve
675
developing a methodology for determining the approximate location of a burst within a DMA.
676
ACKNOWLEDGEMENTS
677
This work is part of the first author’s PhD sponsored by the University of Exeter. The DMA data used
678
in the paper have been collected as part of the Neptune project funded by the UK Engineering and
679
Physical Sciences Research Council (EP/E003192/1) and provided by Mr Ridwan Patel from
680
Yorkshire Water which is gratefully acknowledged. The work presented in this paper has been
681
patented (Publication No. WO/2010/131001PATENT No GB0908184.5.).
21
682
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25
769
LIST OF FIGURES
770
Figure 1. Diagrammatic representation of the Event Recognition System components, subsystems and
771
modules.
772
Figure 2. Artificial Neural Network for the one step ahead prediction of flow/pressure values showing
773
a generic example of a suitable input structure.
774
Figure 3. Simplified structure of the District Metered Area level Bayesian Inference System with
775
examples of the parameters used, when no information about past events is available/considered, in
776
the Conditional Probability Tables associated with some of its nodes.
777
Figure 4. Number of alarms correlated with the real-life events identified by visual inspection of the
778
data with (a), and without (b) using the Evolutionary Algorithm optimisation strategy.
779
Figure 5. Detection of a large burst event with (a), and without (b) using the Evolutionary Algorithm
780
optimisation strategy.
781
Figure 6. Performance comparison between the District Metered Area level Bayesian Inference
782
System with Conditional Probability Table parameters based on domain experts knowledge and with
783
Conditional Probability Table parameters calibrated by using the Engineered Events information.
784
Figure 7. Example of the result obtained from the ERS tests on the synthetic pipe burst events. CPT
785
parameters based on domain experts knowledge (a), and recalibrated CPT parameters (b).
786
26
787
LIST OF TABLES
788
Table 1. Decision variables and associated ranges of variability.
789
Table 2. Engineered Events time schedule and detection times for the two relevant cases considered.
790
Table 3. Synthetic pipe burst events used for the initialisation of the Event Recognition System and
791
the (re)calibration of the District Metered Area level Bayesian Inference System.
792
Table 4. Synthetic pipe burst events used for testing the Event Recognition System, and test results for
793
the three relevant cases considered.
794
27
795
Table 1. Decision variables and associated ranges of variability.
Decision variable
Range
of
values
used in optimisation
Number of hidden neurons
10 - 100
Number of training cycles
50 - 500
Coefficient of Weight Decay Regularisation
10-5 - 103
Lag Size
4 - 72
Time of the Day
use/do not use
Day of the Week
use/do not use
796
28
797
Table 2. Engineered Events time schedule and detection times for the two relevant cases considered.
Alarm start time
domain experts based
CPT parameters
20/07/2009 - 08:00
July
22/07/2009 - 06:15
24/07/2009 - 16:15
17/08/2009 - 08:30
August 21/08/2009 - 08:00
26/08/2009 - 08:00
01/03/2010 - 21:00
March
02/03/2010 - 21:00
15/03/2010 - 07:45
Alarm start time
calibrated
CPT parameters
20/07/2009 - 08:00
22/07/2009 - 06:15
24/07/2009 - 16:15
17/08/2009 - 08:30
21/08/2009 - 07:30
26/08/2009 - 08:00
01/03/2010 - 9:30
02/03/2010 - 9:30
15/03/2010 - 07:30
798
29
Hydrant opened
time
Hydrant closed
time
20/07/2009 - 08:00
22/07/2009 - 06:05
24/07/2009 - 16:00
17/08/2009 - 08:20
21/08/2009 - 07:20
26/08/2009 - 07:55
01/03/2010 - 09:10
02/03/2010 - 08:00
15/03/2010 - 07:20
21/07/2009 - 08:00
23/07/2009 - 08:00
25/07/2009 - 16:00
18/08/2009 - 07:05
22/08/2009 - 08:05
27/08/2009 - 07:00
02/03/2010 - 07:50
03/03/2010 - 07:10
16/03/2010 - 07:15
Table 3. Synthetic pipe burst events used for the initialisation of the Event Recognition System and
800
the (re)calibration of the District Metered Area level Bayesian Inference System.
DMA level BIS recalibration
DMA level BIS calibration
ERS initialisation
799
Event started
Event ended
Duration
[hours]
Flow
[l/s]
Flow
[% average
DMA inflow]
01/02/2012 02:00
01/02/2012 03:45
2.00
2
4.8
02/02/2012 06:00
02/02/2012 15:45
10.00
5
12.0
03/02/2012 09:00
03/02/2012 12:45
4.00
20
48.0
04/02/2012 18:00
04/02/2012 18:45
1.00
10
24.0
06/02/2012 07:00
06/02/2012 10:45
4.00
50
119.9
09/02/2012 05:00
09/02/2012 09:45
5.00
5
12.0
10/02/2012 19:00
10/02/2012 23:45
5.00
10
24.0
12/02/2012 08:00
12/02/2012 08:45
1.00
1
2.4
12/02/2012 13:00
12/02/2012 13:45
1.00
5
12.0
13/02/2012 22:00
13/02/2012 23:45
2.00
15
36.0
15/02/2012 02:00
15/02/2012 07:45
6.00
1
2.4
16/02/2012 00:00
-
instantaneous
20
48.0
16/02/2012 12:00
16/02/2012 14:45
3.00
30
71.9
17/02/2012 03:00
17/02/2012 03:45
1.00
1
2.4
18/02/2012 14:00
18/02/2012 16:45
3.00
2
4.8
19/02/2012 07:00
19/02/2012 19:45
13.00
15
36.0
20/02/2012 23:00
21/02/2012 01:45
3.00
5
12.0
21/02/2012 17:00
21/02/2012 19:45
3.00
8
19.2
21/02/2012 22:00
21/02/2012 23:45
2.00
2
4.8
22/02/2012 05:00
22/02/2012 05:45
1.00
20
48.0
23/02/2012 18:00
-
instantaneous
40
95.9
24/02/2012 01:00
24/02/2012 04:45
4.00
2
4.8
25/02/2012 10:00
25/02/2012 10:45
1.00
10
24.0
25/02/2012 19:00
25/02/2012 20:45
2.00
2
4.8
26/02/2012 17:00
26/02/2012 17:45
1.00
1
2.4
27/02/2012 15:00
28/02/2012 04:45
14.00
10
24.0
28/02/2012 15:00
28/02/2012 16:45
2.00
2
4.8
29/02/2012 10:00
29/02/2012 13:45
4.00
1
2.4
801
30
the three relevant cases considered.
Event started
Event ended
Event
duration
[hours]
Flow
[l/s]
Flow
%
average
DMA
inflow
Recalibrated
CPT parameters
803
Calibrated
CPT parameters
Table 4. Synthetic pipe burst events used for testing the Event Recognition System, and test results for
Domain experts based
CPT parameters
802
Event detected?
01/03/2012 00:00
01/03/2012 07:45
8.00
40
95.9
yes
yes
yes
01/03/2012 10:00
01/03/2012 10:45
1.00
1
2.4
no
no
no
02/03/2012 20:00
02/03/2012 22:45
3.00
3
7.2
yes
yes
yes
04/03/2012 01:00
04/03/2012 02:45
2.00
1
2.4
no
no
yes
04/03/2012 16:00
04/03/2012 20:45
5.00
15
36.0
yes
yes
yes
05/03/2012 18:00
05/03/2012 19:45
2.00
20
48.0
yes
yes
yes
06/03/2012 00:00
06/03/2012 03:45
4.00
1
2.4
yes
yes
yes
07/03/2012 07:00
07/03/2012 10:45
4.00
3
7.2
yes
yes
yes
08/03/2012 15:00
08/03/2012 17:45
3.00
2
4.8
no
no
yes
10/03/2012 00:00
10/03/2012 09:45
10.00
1-40
2.4-95.9
yes
yes
yes
11/03/2012 02:00
11/03/2012 11:45
10.00
2
4.8
yes
yes
yes
12/03/2012 11:00
12/03/2012 11:45
1.00
5
12.0
no
yes
yes
13/03/2012 09:00
13/03/2012 09:45
1.00
10
24.0
yes
yes
yes
13/03/2012 14:00
13/03/2012 15:45
2.00
5
12.0
yes
yes
yes
13/03/2012 22:00
13/03/2012 22:45
1.00
2
4.8
no
no
yes
15/03/2012 11:00
15/03/2012 11:45
1.00
2
4.8
no
no
yes
15/03/2012 19:00
16/03/2012 00:45
6.00
5
12.0
yes
yes
yes
16/03/2012 18:00
16/03/2012 18:45
1.00
1
2.4
no
no
no
17/03/2012 15:00
17/03/2012 19:45
5.00
15
36.0
yes
yes
yes
19/03/2012 01:00
19/03/2012 08:45
8.00
1
2.4
yes
yes
yes
19/03/2012 17:00
21/03/2012 05:00
36.00
3
7.2
yes
yes
yes
26/03/2012 16:15
26/03/2012 16:45
0.75
3
7.2
no
no
no
27/03/2012 01:00
27/03/2012 06:45
6.00
10
24.0
yes
yes
yes
28/03/2012 05:00
28/03/2012 05:45
1.00
5
12.0
no
yes
yes
29/03/2012 00:00
29/03/2012 00:45
1.00
70
167.9
yes
yes
yes
30/03/2012 01:00
30/03/2012 03:45
3.00
2
4.8
no
yes
yes
30/03/2012 23:00
31/03/2012 00:45
2.00
5
12.0
no
yes
yes
31/03/2012 15:00
31/03/2012 21:45
7.00
8
19.2
yes
yes
yes
11
7
3
39
25
11
31
Missed
Events
Missed
%
Figure 1. Diagrammatic representation of the Event Recognition System components, subsystems and modules.
32
1
2
Figure 2. Artificial Neural Network for the one-step ahead prediction of flow/pressure values showing
3
a generic example of a suitable input structure.
33
1
2
Figure 3. Simplified structure of the District Metered Area level Bayesian Inference System with
3
examples of the parameters used, when no information about past events is available/considered, in
4
the Conditional Probability Tables associated with some of its nodes.
34
1
2
Figure 4. Number of alarms correlated with the real-life events identified by visual inspection of the
3
data with (a), and without (b) using the Evolutionary Algorithm optimisation strategy.
35
1
2
3
Figure 5. Detection of a large burst event with (a), and without (b) using the Evolutionary Algorithm
4
optimisation strategy.
36
1
2
Figure 6. Performance comparison between the District Metered Area level Bayesian Inference
3
System with Conditional Probability Table parameters based on domain experts knowledge and with
4
Conditional Probability Table parameters calibrated by using the Engineered Events information.
5
37
1
2
Figure 7. Example of the result obtained from the ERS tests on the synthetic pipe burst events. CPT
3
parameters based on domain experts knowledge (a), and recalibrated CPT parameters (b).
38