Extremely Sensitive Anomaly Detection in Pipe Networks Using a Higher-Order Paired-Impulse Response Function with a Correlator

Water distribution systems (WDS) typically consist of buried pipes that deteriorate with age. One of the consequences of deterioration is pipe failures, which can lead to water supply and traffic interruptions, property damage, and also, may result in a reduced public sentiment for water utilities. Subsequent repair of third-party buried telecommunications and power infrastructure caused by the pipe failure may also cause further interruptions and economic losses. Another issue in aged WDS is blockages due to tuberculation, which may significantly reduce the efficiency of water transmission. Therefore, anomaly detection (mainly leaks, blockages, and deteriorations) of underground pipe networks is essential for targeted and preventative pipe maintenance.

During the last 3 decades, hydraulic transient-based detection methods have been developed to detect different anomalies in WDS (Colombo et al. 2009). The principle of this class of methods is akin to the use of radar or sonar waves to detect remote objects. Controlled small-magnitude transient pressure waves can be injected into a pipe, and the existing anomalies can be detected by analyzing the wave reflections induced. Anomalies with a limited spatial extent can be analyzed as lumped elements, such as a leak. Frequency response diagram (FRD) analysis (Lee et al. 2006; Sattar and Chaudhry 2008; Duan et al. 2011); cepstrum analysis (Taghvaei et al. 2006; Shucksmith et al. 2012); transient damping method (Wang et al. 2002); inverse transient analysis (Liggett and Chen 1994; Kim 2005; Vítkovský et al. 2007; Covas and Ramos 2010; Capponi et al. 2017); time-domain reflectometry (TDR) methods (Brunone 1999; Ferrante and Brunone 2004); impulse response function (IRF) analysis (Liou 1998; Nguyen et al. 2018; Wang et al. 2020); the matched-field processing method (Wang and Ghidaoui 2018; Wang et al. 2019); and the paired-IRF method (Zeng et al. 2020a) can be used to detect such localized anomalies.

For extended anomalies with nonuniform properties, such as extended blockages and wall deterioration, the reconstructive method of characteristics (Gong et al. 2014), inverse transient analysis (Stephens et al. 2013), approximate inverse scattering technique (Jing et al. 2018), area reconstruction method (Blasten et al. 2019; Zouari et al. 2020) and layer-peeling method (Zeng et al. 2018, 2019) can be applied to estimate the properties of the extended anomaly.

Among the methods outlined in the preceding paragraphs, the paired-IRF method shows an extremely sensitive detection capability, which has been demonstrated in experiments on a single copper pipe (Zeng et al. 2020a). In this method, persistent pressure waves, such as discharge-induced hydraulic noise, were injected into the pipe instead of using a discrete sharp controlled small-magnitude transient wave (Gong et al. 2018), which is typically used in conventional hydraulic transient-based methods. For this method, a pair of pressure transducers were installed close to the transient generator. The measured pressure traces contain the injected wave and wave reflections. A deconvolution process was then applied to the two measured pressure traces. Because the deconvolution operation is equivalent to division in the frequency domain, it normalizes the pressure traces and reconfigures the complicated pressure waves into impulse responses in the form of simple spikes, which represent the wave injection and wave reflections by the anomalies. However, only the principal (first-order) wave reflections in the paired-IRF trace have been studied previously, with some visible higher-order reflections being neglected by Zeng et al. (2020a). The order of the wave reflection is defined as the number of times that the injected wave has been reflected off a discontinuity. Without a clear accounting of these higher-order reflections, they may be incorrectly treated as the spikes induced by extra anomalies, leading to misdiagnosis.

Laboratory validations of existing hydraulic transient-based anomaly detection methods have been mostly conducted on single pipelines under controlled conditions. Usually, the base pressure in the pipe was held constant by connection to a statically controlled pressure vessel (Meniconi et al. 2013; Ferrante et al. 2014; Nguyen et al. 2018; Wang et al. 2019; Capponi et al. 2020; Zeng et al. 2020a). Experiments with real hydraulic noise and background pressure fluctuations, which are defined as background noise in this current paper, have been rarely conducted to examine the robustness of the transient-based methods. When the effect of the background noise is sufficiently strong to adversely affect the detection results, then new signal-processing methods are needed to further enhance detectability.

The research reported in this paper presents the analytical derivation of a paired-IRF that considers the higher-order wave reflections to an arbitrary order. The higher-order paired-IRF equation clearly explains some visible higher-order spikes on the paired-IRF trace and aids in avoiding misdiagnosis. To further relieve the adverse impact of background noise, a correlation technique, referred to as a correlator, has been developed based on the features of the spikes in the paired-IRF trace to enhance the detectability of the paired-IRF method. The paper presents an experimental study on a small-scale looped pipe network, which has been modified from a single copper laboratory pipe and connected to the municipal water supply (details can be found in the “Experimental Validation on a Looped Pipe Network” section).

The new design of the pipe system provides realistic background noise and a network configuration that makes the application of many existing transient-based detection methods more difficult but which exists in real WDS. Experimental results using hydraulic noise as the injected waves demonstrate that the higher-order paired-IRF can accurately detect very small anomalies inducing small wave reflections (as small as 0.5% of the magnitude of the injected wave) in the pipe network in a noisy environment. The magnitude of the injected pressure wave can be as small as 20 mm even when the background pressure fluctuations reach 2 m. The detection method is extremely sensitive for anomaly detection. The application of the advanced correlator results in a distinctive detector of the anomalies even when the paired-IRF is significantly contaminated by noise.

The system configuration of the paired-IRF method is given in Fig. 1 to illustrate the basic methodology. The corresponding block diagram is also shown in Fig. 1, which illustrates the wave propagation process in the pipe. A pressure wave generator (G) persistently emitting pressure waves into the pipeline is installed in the pipe, and a pair of pressure transducers ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are installed at the right side of the generator (without loss of generality). The pipe section of interest is to the right of ${\mathrm{P}}_1$ (${\mathrm{P}}_1–\mathrm{B}$). The boundaries of the pipe are assumed to be arbitrary, such as junctions in a pipe network, or a valve and a reservoir in a single pipe system. The terms $H_1$ and $H_2$ are defined as the transfer functions of Section $\mathrm{G}–{\mathrm{P}}_1$ and Section ${\mathrm{P}}_1–{\mathrm{P}}_2$, respectively. The term $R$ represents the impulse response function in the frequency domain, with the subscripts $L$ and $R$ referring to the pipe at the left side and right side of ${\mathrm{P}}_1$.

The paired-IRF method was first developed by Zeng et al. (2020a) with only first-order wave reflections being considered. In the current paper, a new-generation paired-IRF method is proposed to include all higher-order wave reflections.

According to the block diagram in Fig. 1, the pressures $P_1$ and $P_2$ can be writtenwhere plus-sign and minus-sign superscripts = positive direction (left to right from ${\mathrm{P}}_1$ to ${\mathrm{P}}_2$) and negative direction (right to left from ${\mathrm{P}}_2$ to ${\mathrm{P}}_1$), respectively. By assuming $P_0(j\omega )$ is the original pressure wave caused by the generator without any reflections and according to Fig. 1, the directional pressure waves $P_1^{+}$ and $P_1^{-}$ considering all higher-order wave reflections can be written

A rearrangement of Eqs. (3) and (4) gives explicit expressions for ${\mathrm{P}}_1^{+}$ and ${\mathrm{P}}_1^{-}$ as follows:

Substituting Eqs. (5) and (6) into Eqs. (1) and (2) yieldswhere a further division of $P_2$ by $P_1$ gives

To further explore the physical meaning of the equation, it is expanded using a Taylor series expansion as follows:in which the first-order and all higher-order ($\ge 2$) wave reflections are clearly presented. By neglecting the higher-order wave reflections, Eq. (10) can be simplified towhich is identical with the result of Zeng et al. (2020a). By defining the one-way travel time of the pressure wave in the Section ${\mathrm{P}}_1$ to ${\mathrm{P}}_2$ as $¯t$, the term $1/H_2$ in the brackets, for a lossless system, means transferring the IRF forward in time by a value of $¯t$, whereas $-H_2$ in the brackets means reversing the sign of the IRF after delaying it by time $¯t$. Thus, $P_2/P_1$, after transforming into the time domain, consists of a pair of superimposed IRFs and herein is defined as the paired-IRF.

Eqs. (10) and (11) give the frequency-domain transfer function of the paired-IRF, so accordingly, the time-domain paired-IRF $P_2/P_1$ from Eqs. (10) and (11) can be calculated using a least-squares deconvolution (Nguyen et al. 2018) or a truncated singular value decomposition (Forbes et al. 2003).

A simple numerical case for a reservoir-pipeline-valve system is presented in this section to illustrate the process to design a correlator. The simulated pipe system of 180 m in length is shown in Fig. 2 and is used to demonstrate the method. Two pressure transducers in close proximity (distance apart of $L_p=1\mathrm{m}$ in this case) are used in the paired-IRF method. The first transducer, ${\mathrm{P}}_1$, and pressure wave generator, G, are located 80 m away from the reservoir, which has a constant water head of 60 m. The generator is simulated by an emitter (an orifice discharging to the atmosphere) with its discharge area alternating over time. In this case, the pressure wave generator was set to follow a white-noise sequence. The valve at the other end of the pipe is partially open and has a base flow rate of $0.02{\mathrm{m}}^3/\mathrm{s}$ for steady-state conditions. The internal diameter of the pipeline is assumed to be 120 mm, the wave speed $a$ is $\mathrm{1,000}\mathrm{m}/\mathrm{s}$, and the Darcy-Weisbach friction factor $f$ is 0.02.

Unsteady friction is not considered in the simulation. A circular leak with a diameter of 6 mm is assumed to exist 50 m downstream of ${\mathrm{P}}_1$. The flow rate out of the leak is $0.84\mathrm{L}/\mathrm{s}$ with the flow coefficient $C_d=0.9$. The method of characteristics (Wylie and Streeter 1993) with a time step of 0.1 ms has been applied to simulate the pressures as shown in Fig. 3.

A looped copper pipe network system has been designed in the Robin Hydraulics Laboratory at the University of Adelaide. Laboratory experiments have been conducted on the system to validate the higher-order paired-IRF and the advanced correlator.

A higher-order paired-impulse response function (IRF) has been derived to identify anomalies in pipe networks with a high degree of sensitivity. It transforms the micropressure waves of complicated waveforms into discrete spikes and considers both the principle and higher-order wave reflections caused by the anomalies. Visible higher-order spikes on the paired-IRF trace can be clearly explained using the new higher-order paired-IRF equation to avoid misdiagnosis of anomalies. An advanced correlator has then been designed building on the paired-IRF trace. It highlights the paired spikes induced by anomalies in the paired-IRF trace and suppresses spikes associated with noise.

Extensive laboratory experiments have been conducted on a looped pipe network. The looped pipe system provides an uncontrolled network configuration with real background noise from the mains for the tests. Experimental results show that the paired-IRF method is capable of accurately detecting small anomalies that reflect only 0.5% of the incident wave in a network configuration in the presence of background noise contaminating the measured pressures. The higher-order paired-IRF equation successfully explains the second-order wave reflections observed in the experimental results.

Sensitivity analyses show an appropriate magnitude of the persistent pressure waves, which leads to a sufficient signal to noise ratio but does not excite strong pipe wall vibration, results in the maximum sensitivity of the detection. However, the sensitivity is great enough (detectable to wave reflections at 1% of the injected wave) even when the magnitude of the injected pressure waves is only 20 mm with the background pressure fluctuations reaching 2 m. The correlator applied to the experimental paired-IRF traces with its controlled parameters properly tuned further improves the sensitivity.

The persistent pressure waves used in proposed methods can be simply generated by opening a side discharge valve in the laboratory and potentially in the field without using any active transient generator. Different anomalies, such as leaks, blockages, and wall-deteriorated sections, which are essentially impedance changes that induce wave reflections, can all be detected using the proposed methods. Overall, the practical operability, high degree of sensitivity, and wide scope of application of the paired-IRF with the correlator indicate its high practical value in real applications.

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

The research presented in this paper has been supported by the Australian Research Council through the Discovery Project Grant DP190102484. The authors thank technicians Mr. Brenton Howie and Mr. Simon Golding for their support in the experimental work.