Hydraulic Transient Wave Separation Algorithm using

This is a pre-print (pre-refereeing) copy of the manuscript. The final version has been published by the Journal of Hydroinformatics. Shi, H., Gong, J., Zecchin, A. C., Lambert, M. F., and Simpson, A. R. (2017). "Hydraulic transient wave separation algorithm using a dual-sensor with applications to pipeline condition assessment." Journal of Hydroinformatics, Available Online: 2017 Jul, jh2017146; DOI: 10.2166/hydro.2017.146

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Hydraulic Transient Wave Separation Algorithm using Dual-sensors with

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Applications to Pipeline Condition Assessment

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He Shi1, Jinzhe Gong2, Aaron C. Zecchin3, Martin F. Lambert4 and Angus R. Simpson5

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Adelaide, SA 5005, Australia; Email: [email protected]

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2

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University of Adelaide, SA 5005, Australia; Email: [email protected]

Ph.D. Candidate; School of Civil, Environmental and Mining Engineering, University of

Postdoctoral Research Fellow; School of Civil, Environmental and Mining Engineering,

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3

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Adelaide, SA 5005, Australia; Email: [email protected]

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4

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SA 5005, Australia; Email: [email protected]

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5

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SA 5005, Australia; Email: [email protected]

Senior Lecturer; School of Civil, Environmental and Mining Engineering, University of

Professor; School of Civil, Environmental and Mining Engineering, University of Adelaide,

Professor; School of Civil, Environmental and Mining Engineering, University of Adelaide,

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ABSTRACT

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Over the past two decades, techniques have been developed for pipeline leak detection and

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condition assessment using hydraulic transient waves (i.e. water hammer waves). A common

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measurement strategy for applications involves analysis of signals from a single pressure


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sensor located at each measurement site. The measured pressure trace from a single sensor is a

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superposition of reflections coming from upstream, and downstream, of the sensor. This

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superposition brings complexities for signal processing applications for fault detection analysis.

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This paper presents a wave separation algorithm, accounting for transmission dynamics, which

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enables the extraction of directional traveling waves by using two closely placed sensors at one

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measurement site. Two typical transient incident pressure waves, a pulse wave and a step wave,

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are investigated in numerical simulations and laboratory experiments. Comparison of the wave

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separation results with their predicted counterparts shows the wave separation algorithm is

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successful. The results also show that the proposed wave separation technique facilitates

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transient-based pipeline condition assessment.

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Keywords: hydraulic transient; pipeline condition assessment; unsteady flow; water hammer;

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wave separation.

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Introduction

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The aging of water distribution systems worldwide has brought many issues, ranging from

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significant water and energy losses (Colombo & Karney 2002) to risks to public health due to

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possible pathogen intrusion (Karim et al. 2003). Over the past two decades, hydraulic transients

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(water hammer waves) have been identified as a useful tool for non-invasive pipeline leak

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detection (Mpesha et al. 2001; Ferrante & Brunone 2003; Covas et al. 2005; Lee et al. 2005;

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Soares et al. 2011; Ferrante et al. 2013; Duan 2016), blockage detection (Sattar et al. 2008;

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Meniconi et al. 2013; Massari et al. 2014), wall condition assessment (Gong et al. 2013;


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Stephens et al. 2013) and general system parameter identification (Zecchin et al. 2013; Zecchin

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et al. 2014a). When undertaking a hydraulic transient analysis of a pipeline system, a transient

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disturbance (a pulse or a step pressure wave) is typically introduced by abruptly operating a

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valve. Then the transient pressure wave propagates along the pipe in both upstream and

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downstream directions. Any physical changes or anomalies in a pipeline will affect the

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propagation of transient pressure waves, resulting in specific reflections. These reflections can

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be analysed in either the time domain or in the frequency domain, in order to diagnose the

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anomalies in the pipeline system.

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Most existing studies are based on the analysis of the transient pressure measured by a single

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sensor, or by multiple sensors usually separated by a significant distance along a pipe.

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However, transient waves usually travel along a pipe in two directions. The hydraulic pressure

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at any single point in a pipeline can be expressed as the sum of a traveling pressure wave

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coming from upstream of the measurement point, and a traveling pressure wave coming from

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downstream. As a consequence, for a single pressure sensor, the measured signal is always a

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superimposed signal of the waveforms propagating upstream and downstream. One

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measurement strategy to avoid a superposition problem is by placing the measurement point at

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a dead end to ensure the reflection comes only from one direction (Gong et al. 2014). However,

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when investigating transmission mains, which may be tens of kilometers long, it is not always

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practical to find an ideal measurement point at a dead end. Moreover, when multiple anomalies

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exist on both sides of a sensor, which is the common case in most pipelines, the measured

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pressure signal can be very complex and difficult to interpret, even when multiple measurement

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sites are used (Gong et al. 2016).


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To investigate and extract the directional information of traveling transient pressure waves,

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Gong et al. (2012a) proposed a technique that uses two pressure sensors (100 m spaced) to

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separate the pressure waves traveling downstream from those traveling upstream along a

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pipeline. In a subsequent study by Gong et al. (2012b), a new measurement strategy, which

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involved the use of two pressure sensors in close proximity (1 m spaced), was proposed to

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facilitate the wave separation. However, these preliminary studies were limited to numerical

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simulations with ideal conditions where the pipeline between two sensors is assumed to be

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lossless and the incident wave is a sharp step signal. These ideal conditions, however, do not

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hold in real pipeline systems.

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Zecchin et al. (2014b) proposed a technique for extracting the impulse response of a single

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pipeline using a pair of sensors (10 m spaced) for measurement, taking into account hydraulic

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noise (in the form of wide-sense stationary pressure signals) as the form of excitation. In that

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study, a theoretical propagation loss between two sensors was considered, however, directional

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traveling waves were not explicitly analysed. The wide-sense stationary pressure signals are

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difficult to achieve in practice, and only a numerical case study was conducted in that study.

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It should be noted that the use of dual-sensors in close proximity for wave separation has been

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studied in the acoustic research area, where acoustic waves measured by two or more

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microphones are analysed in ducts (Chung & Blaser 1980). However, hydraulic transient waves

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are typically different from acoustic waves in signal bandwidth and magnitude. Except for the

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preliminary numerical work reported in Gong et al. (2012a,b), to the knowledge of the authors,

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there is no study on the separation of hydraulic transient waves in pressurised pipelines.


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The research reported in the current paper develops a systematic wave separation algorithm

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that can extract the two directional traveling hydraulic transient waves from pressure traces as

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measured by two closely spaced pressure sensors. Based on the preliminary work in Gong et

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al. (2012a,b) and Zecchin et al. (2014b), this paper focuses on solving practical limitations of

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these approaches when applying wave separation to real pipelines. The new development

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includes: (1) techniques for estimating the transmission loss between two sensors; (2) the

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removal of the dependence of the incident wave (for discrete incident waves) in the algorithm;

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and (3) verification of the wave separation technique by laboratory experiments.

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To validate the wave separation algorithm, a pulse incident wave is used in a numerical study

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and a step wave is considered in a laboratory study. In both studies, as presented in this paper,

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the comparison between the extracted directional reflection trace with its counterpart, which

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has a reflection from one direction only, shows the wave separation algorithm is successful.

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The wave separation algorithm provides the directional information of traveling transient

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pressure waves in pipelines and simplifies the complex reflections caused by wave

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superposition. The directional waves, as obtained in the laboratory study, are then used to

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determine the properties of two deteriorated pipe sections in the experimental system

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(simulated by short pipe sections with thinner wall thicknesses). The results demonstrate that

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the proposed wave separation technique can significantly facilitate transient-based pipeline

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condition assessment.

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This paper is structured as follows. The wave separation algorithm is introduced in Section 2.

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Section 3 outlines the numerical simulation tests to evaluate the proposed method using a pulse

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pressure wave as the excitation. In Section 4, experimental data involving a step wave as the


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excitation is used to validate the performance of the wave separation algorithm. Finally, the

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discussions and conclusions are made in Sections 5 and 6.

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Wave Separation Algorithm using Dual-sensors

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This section outlines the wave separation algorithm using the original pressure data measured

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by two closely placed pressure sensors (dual-sensors). Section 2.1 provides the hydraulic wave

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propagation theory, in which the basic wave separation algorithm is given. Following is the

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determination of transfer function between two sensors in Section 2.2. In this section, to inspect

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the dynamic characteristics of the pipe section between two sensors, both analytic expression

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and empirical estimation of the transfer function are explored. To obtain the directional

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traveling waves (i.e. reflected waveforms), the dependence of the incident waves is removed

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which is described in Section 2.3. An approach for applying the wave separation algorithm in

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pipelines is also given in Section 2.3.

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Hydraulic wave propagation theory

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Using linear system theory and a one-dimension (one-D) water hammer model for water

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transient analysis (Wylie & Streeter 1993; Chaudhry 2014), the hydraulic pressure at any single

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point in a pipeline can be expressed as the sum of a positive traveling pressure wave coming

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from upstream of the point, and a negative traveling pressure wave coming from downstream

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of the point, i.e.

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p ( x, t )  p  ( x, t )  p  ( x , t )

(1)


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where p is the total pressure as measured by a sensor, p  is the positive pressure wave

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coming from the upstream, p  is the negative pressure wave traveling from the downstream

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to the upstream, x is the axial coordinate along the pipe and t is time.

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Applying the Laplace transform to Eq.(1) to transform the signals into the Laplace (or

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frequency) domain, the pressure signal is then described as

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P( x, s )  P  ( x , s )  P  ( x , s )

(2)

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where s is the complex valued frequency (the Laplace variable), and the capital P represents

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pressure signals in the frequency domain.

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Fig. 1. (a) Proposed configuration for the pressure transient test with dual-sensors in a pipeline;

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and (b) Corresponding block diagram in the frequency domain illustrating the wave

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propagation. (Note, LTI System = Linear Time Invariant System).

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A typical configuration for transient pressure measurement using dual-sensors in a pipeline is

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given in Fig. 1(a): a side discharge valve G is used as the transient generator, T1 and T2 are the

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pressure sensors, and p1 (t ) and p2 (t ) are the measured pressure traces by T1 and T2,

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respectively. The pipe section between T1 and T2 is assumed to act as a linear time-invariant

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(LTI) system (Ljung 1999), where the pressures p1 (t ) and p2  (t ) are the positive traveling

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waves at T1 and T2, respectively, and p1 (t ) and p2  (t ) are the negative traveling waves at T1

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and T2, respectively.

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The configuration can be described by a block diagram as shown in Fig. 1(b). A transfer

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function H ( s) is the representation of the wave propagation dynamics between sensor T1 and

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T2, where P1 ( s ) and P2 ( s) are the Laplace transforms of p1 (t ) and p2 (t ) respectively (as for

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all other capitalised symbols). Based on Eq.(2), P1 ( s ) and P2 ( s) can be written as the sum of

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the positive and the negative traveling waves as in Eqs. (3) and (4).

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P1 ( s)  P1 ( s)  P1 ( s)

(3)

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P2 ( s)  P2  ( s)  P2  ( s)

(4)

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The outputs of the system [ P1 ( s ) and P2  ( s ) ] and the inputs of the system [ P2  ( s ) and

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P1 ( s ) ] are related by the transfer function H ( s) and written as

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P1 ( s)  P2  ( s) H ( s)

(5)


P2  ( s)  P1 ( s) H ( s)

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157

(6)

Substituting Eqs. (5) and (6) into Eqs. (3) and (4), respectively, yields

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P1 ( s)  P1 ( s)  P2  ( s) H ( s)

(7)

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P2 ( s)  P1 ( s) H ( s)  P2  ( s)

(8)

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P2  ( s ) can be eliminated by multiplying Eq. (8) by H ( s) and then subtracting Eq. (7) from

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the resulting equation, yielding the final result

P1 ( s ) 

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P1 ( s)  P2 ( s ) H ( s ) 1  H 2 ( s)

(9)

Substituting Eq. (9) into Eq. (3) and rearranging gives

P1 ( s) 

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P2 ( s ) H ( s )  P1 ( s) H 2 ( s) 1  H 2 ( s)

(10)

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From Eqs. (9) and (10), the positive traveling wave P1 ( s ) and negative traveling wave P1 ( s )

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can be extracted from the original pressure measurements [ P1 ( s ) and P2 ( s) ] using the transfer

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function H ( s) in the transform domain.

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Determination of the transfer function H(s)

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Analytic representation


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The transfer function H ( s) is a characterisation of the physical wave propagation dynamics of

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the pipe section. In one-D water hammer analysis, the transfer function H ( s) for the pipe

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between two sensors can be expressed analytically as (Wylie & Streeter 1993)

H ( s)  e ( s )l

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(11)

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where l is the length between two sensors,  ( s) is the propagation operator that describes the

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frequency dependent attenuation and phase change per unit length,  ( s) is a complex function

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of s that independent of l .  ( s) can be expressed in a general form by (Zecchin 2009)

 ( s) 

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1 a

 s  R( s) s  C ( s)

(12)

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where a is the wave speed, R  s  and C  s  represent the resistance and compliance terms,

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respectively. If only steady friction and elastic pipe behaviour are considered, C ( s)  0 , and

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R  s   R is given by (Zecchin 2009)

fQ DA

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R

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where f is the Darcy-Weisbach friction factor, Q is the steady-state flow, D is the diameter

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of the pipe, and A is the cross-sectional area of the pipe.

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From a practical perspective, using the analytic form (11), H(s) can be completely specified

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using measured values of l, a, and a calibrated value of R (or known D with estimates of Q and

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f ).

(13)


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Empirical Representation

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As an alternative to the analytic expression for H(s), the properties of the transfer function can

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also be determined empirically. In hydraulic transient analysis, a pipeline system is typically

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excited by abruptly opening or closing a valve, which results in a discrete wave with a short

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duration as an incident pressure wave (e.g. a sharp step or pulse wave). Under these conditions,

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an assumption can be made that during the time of the incident wave entering into the system

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at T1 then exiting the system at T2, there are no transient waves entering the system from T2

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[i.e. p2  (t )  0 in Fig. 1]. This assumption is often valid when the incident wave is short, and

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the system is excited from a steady state condition. Therefore, the LTI system in Fig. 1(a) can

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be temporarily treated as a single-input and single-output system for this short time period. The

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input is the incident wave p1 (t )  p1i (t ) at T1, and the output is the incident wave

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p2  (t )  p2i (t ) at T2. The transfer function H ( s) is the linear mapping from an input to an

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output in the Laplace domain, and can be given by

H ( s) 

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P2i ( s ) P1i ( s )

(14)

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where P1i ( s ) and P2i ( s) are the time-windowed Laplace transforms of the incident wave at

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T1 and T2, respectively. In this context, time-windowed means that, only the time period before

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reflections from the external pipe system enter the section of interest is considered. That is, in

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the time domain, when the incident wave is a discrete wave within a short duration, the incident

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waves p1i (t ) and p2i (t ) can be extracted from the original measured pressure trace p1 (t ) and

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p2 (t ) by applying a rectangular window and excluding any reflections.

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The wave separation algorithm


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In Fig. 1(a), when an incident pressure wave is generated at G and arrives at sensor T1, the

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positive traveling pressure wave at T1 contains the incident wave and the reflected wave

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coming from upstream of T1. The reflected wave is the focus because it carries the pipeline

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information that can be used for pipeline condition assessment. However, compared to the

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incident wave, the reflections are usually much smaller in size. Given this, removing the

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dependence of the incident wave from the wave separation results leads to clearer results, and

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the method is described below.

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In Fig. 1(a), the positive traveling waves can be written as the sum of the incident wave and

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the reflected wave coming from upstream.

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p1 (t )  p1i (t )  p1r  (t )

(15)

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p2  (t )  p2i (t )  p2 r  (t )

(16)

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where p1r  (t ) and p2 r  (t ) are the reflected waves coming from upstream of the

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measurement points T1 and T2 respectively. The negative traveling waves p1 (t ) and p2  (t )

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can be written as the negative traveling reflected waves p1r  (t ) and p2 r  (t ) .

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p1 (t )  p1r  (t )

(17)

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p2  (t )  p2 r  (t )

(18)

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As a result, the pressure waves as measured by the sensors at points T1 and T2 can be described

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by


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p1 (t )  p1i (t )  p1r (t )

(19)

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p2 (t )  p2i (t )  p2 r (t )

(20)

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where p1r (t )  p1r  (t )  p1r  (t ) and p2 r (t )  p2 r  (t )  p2 r  (t ) . As a sharp step or pulse wave

229

is usually used as an incident wave, and in the time domain, the incident waves , p1i (t ) and

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p2i (t ) , can be easily identified and extracted from the measured pressure traces using a time-

231

windowing procedure as for Eq. (14). Similarly the reflections, p1r (t ) and p2 r (t ) , can also be

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extracted by applying an appropriate rectangular time window. These windows are depicted in

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Fig.3(a).

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Transforming Eqs. (15)-(20), and then substituting the transformed equations and Eq.(14)

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into Eqs. (9) and (10), rearrangement of the final result yields the following wave forms for

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the two reflected wave components

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P1r  ( s) 

P1r ( s)  P2 r ( s) H ( s) 1  H 2 ( s)

P2 r ( s ) H ( s )  P1r ( s ) H 2 ( s ) P1r ( s)  1  H 2 ( s) 

(21)

(22)

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The inverse Laplace transforms of Eqs. (21) and (22) will give the positive traveling reflected

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waves and the negative traveling reflected waves in the time domain.

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For analysis of real pipeline systems where the pressure signals measured by sensors are used,

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the value of the Laplace variable is restricted to the imaginary axis, i.e. s = i , where i is the


243

imaginary unit, and  is the radial frequency. Consequently, the Fourier transform can be used

244

instead of the Laplace transform.

245

To apply the wave separation algorithm to pressure traces [ p1 (t ) and p2 (t ) ] measured by dual-

246

sensors as in Fig.1(a), the following steps will be performed:

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1. Time-windowing to separate incident waves and reflections in the original pressure traces measured by dual-sensors using Eqs. (19) and (20). See Fig. 3(a). 2. Transfer incident waves and reflections into the frequency domain by using the Fourier transform. 3. Determine the transfer function between two sensors using the analytic Eq. (11) or using the empirical Eq. (14).

253

4. Extract the directional reflection waves using Eqs. (21) and (22).

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5. Transfer wave separation results into the time domain using an Inverse Fourier

255

Transform or using separation results directly in the frequency domain.

256

It should be noted that, when other incident waves are used in place of discrete waves with a

257

short duration, step 1 can be ignored and Eqs. (9) and (10) in step 4 used instead. Before the

258

wave separation algorithm is applied to real data, pre-processing may be needed, including

259

determining the effective frequency range to minimise the impact of high frequency noise on

260

the time domain reconstruction of the separated reflected waves.

261

262

Numerical Verification


263

To verify the dual-sensor wave separation algorithm, numerical simulations have been

264

conducted. The focus of the current section is the wave separation for reflections induced by a

265

single pulse incident wave. A step incident wave will be discussed in the experimental

266

verification section. A pulse hydraulic pressure wave is a typical excitation for transient-based

267

pipeline fault detection, but it has never been studied previously for wave separation.

268

System layout and procedure

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For the numerical study, a metallic pipeline system with two short deteriorated sections and

270

one relatively long section with a change of pipe class is considered. The layout of the

271

numerical pipeline system is given in Fig. 2. The physical details of the pipe sections are

272

summarised in Table 1. The system is a reservoir-pipeline-reservoir (R-P-R) system. Reservoir

273

1 has a constant head of 60 m, and the constant head for Reservoir 2 is 57 m. The total length

274

of the pipeline is 1 km. The steady-state flow is calculated as 0.263 m3/s, corresponding to a

275

velocity of 1.34 m/s. For the normal pipe sections, the internal diameter is 500 mm, the wall

276

thickness is 8 mm, and the wave speed is 1154 m/s. Two pipe sections L2 and L9 have thinner

277

wall thicknesses (6 mm and 5 mm), larger internal pipe diameters (504 mm and 506 mm) and

278

smaller wave speeds (1083 m/s and 1036 m/s) are placed in the system to simulate the

279

deteriorated sections (e.g. extended internal corrosion). Pipe section L7 with a length of

280

approximately 150 m, the same internal diameter as the majority of the pipe, but a thinner wall

281

thickness (7 mm) and thus a lower wave speed (1123 m/s), is placed in the system to simulate

282

a section of a lesser pipe class. A significantly higher Darcy-Weisbach friction factor (0.03)

283

has been assigned to sections L2 and L9 to represent the effect of a much higher wall surface

284

roughness as would result from a pipe that has experienced corrosion. The dual sensor (with a


285

sensor spacing of 0.981 m) is placed in the middle of the pipeline system at T1 and T2,

286

respectively. A side-discharge valve which is located at 0.981 m upstream from T1 is used as

287

the transient generator. The steady-state discharge through the side-discharge valve is set as

288

0.01 m3/s. The length of each pipe section has been selected to satisfy the Courant condition

289

for the time domain method of characteristics ( MOC ) simulations so that no interpolation

290

scheme is required (Chaundry, 2014).

Reservoir 1

Reservoir 2 Generator

G (Side-discharge Valve)

L1

L2

L3

T1

T2

L4 L5

L6

L7

L8

L9

Upstream

L10 Downstream

291

Fig. 2. Layout of the pipeline system used in the numerical simulations (not to scale). See Table

292

1 for physical details.

293

Table 1. Physical details of the pipe sections used in the numerical simulations in Fig.2. Link

Length

Internal diameter

(m) L1 L2 L3 L4 L5 L6 L7 L8 L9

415.96 12.02 72.01 0.981 0.981 69.99 150.15 60.01 11.99

( mm ) 500 504 500 500 500 500 500 500 506

Wall thickness (mm) 8 6 8 8 8 8 7 8 5

Wave speed

Friction factor

( m/s ) 1154 1083 1154 1154 1154 1154 1123 1154 1036

(-) 0.017 0.030 0.017 0.017 0.017 0.017 0.017 0.017 0.030


L10

205.99

500

8

1154

0.017

294

295

An incident pressure wave is generated at time t = 0.1 s by manoeuvring the side-discharge

296

valve. The incident wave is a pulse wave with 20 ms duration, generated by fully closing the

297

side discharge valve then fully opening it again (the manoeuvre is designed numerically that

298

the incident pulse pressure wave as generated has a shape similar to a cosine function changing

299

from ̶  to  , to make the signal more realistic than a sharp instantaneous rise). The response

300

of the pipeline system is simulated by the MOC with a time step of 0.05 ms and steady friction

301

only.


302

Wave separation results

(a)

66 64

Time window for reflections

Head (m)

62 (Enlarged below)

60 58 56 Time window for incident wave p1(t) 54 Reflections from reservoirs p2(t) 52 0

0.2

0.4

(b)

0.6 Time (s)

0.8

reflected wave T1,T2

0.4

p1r(t) p2r(t)

0.2 Head (m)

1

0 -0.2 -0.4 0.1

0.2

0.3

0.4

0.5 Time (s)

0.6

0.7

0.8

0.9

303

Fig. 3. (a) Numerical pressure traces measured at T1 and T2; and (b) Enlarged view of the wave

304

reflections from deteriorated sections in the numerical study.

305

The pressure traces at T1 and T2 are used as the measurements p1 (t ) and p2 (t ) , which are

306

shown in Fig. 3(a). The wave separation algorithm is applied to the measurements p1 (t ) and


307

p2 (t ) by following the steps which are outlined in Section 2.3.2. The reflected waves p1r (t )

308

and p2 r (t ) are shown in Fig. 3(b). It can be seen from Fig. 3(b) that the pressure reflections

309

as recorded by dual-sensors possess a complex form of pressure wave fluctuations, although

310

only three uniform sections with lower wave speeds are considered. This complexity is due to

311

the superimposition of the reflections from the three thinner-walled sections.

312

The resultant directional traveling waves are shown in Fig. 4. Fig. 4(a) shows the reflections

313

from upstream of T1 and Fig. 4(b) gives the reflections from downstream. The pressure waves

314

p1r _ A (t ) and p1r _ A (t ) are obtained by using the analytic expression of the transfer function

315

between two sensors according to Eqs. (11) and (12), while p1r _ E  (t ) and p1r _ E  (t ) are

316

calculated from the empirical transfer function which is estimated by using the extracted

317

incident waves according to Eq. (14).

318

For a comprehensive comparison, the wave separation results are compared with predicted

319

results as computed directly from the MOC. The predicted results for upstream reflections

320

[ p1r _ P  (t ) as shown in Fig. 4(a)] are obtained from MOC modelling the system similar to

321

depicted in Fig. 2, but only with one deteriorated section L2 existing on the upstream side of

322

the sensors. On the downstream side of the sensors, there are just uniform intact pipes (i.e. L7

323

and L9 are set as the same as the intact sections). Hence, the simulated reflections only come

324

from upstream and are a result of section L2. Similarly, the predicted results for downstream

325

 reflections [ p1r _ P (t ) as shown in Fig. 4(b)] are acquired by MOC modelling with no defective

326

sections existing on the upstream side of the sensors. So that reflections only happen on the

327

downstream side of the sensors and are a result of sections L7 and L9.


328

(a) 0.2

Reflections from L2 Head (m)

0.1

Secondary reflections

0 p1r_A +(t)

-0.1

p1r_E +(t)

-0.2 0.1

p1r_P +(t)

0.2

0.3

0.4

0.5 Time (s)

0.6

0.7

0.8

0.9

(b) 0.4

Head (m)

0.2

Reflections from L9 Reflections from L7

Secondary reflections

0 p1r_A -(t)

-0.2 -0.4 0.1

p1r_E -(t) p1r_P -(t)

0.2

0.3

0.4

0.5 Time (s)

0.6

0.7

0.8

0.9

329

Fig. 4. (a) Directional reflected pressure waves traveling from upstream to downstream; and

330

(b) Directional reflected pressure waves traveling from downstream to upstream.

331

It can be seen in Fig. 4 that the reflections from the three thinner-walled pipe sections are

332

separated and clearly shown in the directional waves p1r (t ) and p1r (t ) respectively. The

333

separation results from two different transfer function calculation methods (analytical and


334

empirical) are almost identical, and both of them have an excellent match with the MOC

335

predictions. It should be noted that the separated results of directional waves include multiple

336

reflections while the predicted results do not. The multiple reflections are due to secondary

337

reflections between anomalous sections on the two sides of sensors. For example, when all

338

three thinner-walled sections are considered in the simulation, the major wave reflections from

339

sections L7 and L9 [as shown in Fig. 4(b)] will propagate from downstream to upstream, pass

340

the dual-sensors and then be reflected by section L2 as secondary reflections. These secondary

341

reflections will then propagate downstream as part of p1r (t ) . Nevertheless, the numerical

342

simulation demonstrates that the proposed wave separation approach is valid for pipelines

343

excited by single pulse incident pressure waves.

344

Experimental Verification

345

Laboratory experiments have been conducted in a single copper pipeline in the Robin

346

Hydraulics Laboratory at the University of Adelaide. The laboratory pipeline is a one-inch

347

diameter (22.14 mm) copper pipe with a total length of 37.43 m and bounded by two

348

pressurised tanks. The pressurised tanks can be isolated by an in-line valve to make the system

349

a reservoir-pipeline-valve (R-P-V) configuration. The aim of the experimental study is to verify

350

the proposed wave separation technique in real pipelines under controlled conditions.

351

System layout and procedure

352

The layout of the pipeline system used in the experiments is shown in Fig. 5 and the physical

353

details are given in Table 2. The wave speeds are calculated using the theoretical wave speed


354

formula (Wylie & Streeter 1993). The following parameter values are used: Young’s modulus

355

of a copper pipe E  124.1 GPa, restraint factor for the condition of anchored throughout

356

c1  1.006 , bulk modulus of elasticity of water at 15 ℃ K  2.149 GPa, and density of water

357

at 15 ℃   999.1 kg/m3.

358

Closed in-line valve Type B

Pressurized tank T2 T1

G

Type C

a0 e0 D0 9.06 m

a1 e1 D1

a2 e2 D2 5.55m 4.54m

4.02m

4.35m

a0 e0 D0 8.92m

2m

0.99 m 37.43 m

359

360

Fig. 5. System layout of the experimental pipeline system.

361

Table 2. Physical details of the pipeline system used in the laboratory experiments

Pipe Class A B C

Internal diameter Wall thickness Wave speed [symbol = value (mm)] [symbol = value (mm)] [symbol = value (m/s)] D0 = 22.14 e0 = 1.63 a0 = 1319 D1 = 22.96 e1 =1.22 a1 = 1273 D2 = 23.58 e2 = 0.91 a2 = 1217


362 363

The majority of the pipeline is in Class A. Two short pipe sections of Class B and C,

364

respectively, which have thinner wall thicknesses than that of Class A, are placed in the system

365

to simulate pipe sections with wall deterioration. The head in the pressurised tank was

366

controlled at approximately 31 m during the experiments. The in-line valve at the other end

367

was kept closed during the experiments.

368

A solenoid side-discharge valve was used as the transient generator (G) and placed at the same

369

location as pressure sensor T1. The other pressure sensor (T2) was located upstream (on the left)

370

of the transient generator separated by a distance of 0.99 m. A step pressure wave was generated

371

by abruptly closing the solenoid valve in approximately 3 ms. The pressure responses were

372

measured by the two sensors with a sampling frequency of 20 kHz.

373

Wave separation results

374

The original head responses as measured by the dual-sensors are shown in Fig. 6(a). The

375

pressure oscillations before the first boundary reflection are the focus and shown in Fig. 6(b).

376

The steady-state head is determined by averaging a period of measurement before the incident

377

wave and then subtracted from the raw measurements. The start time of the incident wave is

378

set to zero, and the pressure traces are truncated before the boundary reflections (the reflection

379

from the tank and the closed in-line valve). It can be seen that the reflections from the Class B

380

and Class C pipe sections are superimposed in the two measured traces, resulting in complex

381

reflections that are difficult to interpret.


382

(a) p1(t)

Head (m)

40

p2(t)

35 30 25

Boundary Reflections reflections from Class B and C sections

37.64

37.66 37.68 Time (s)

37.7

(b)

Head (m)

6 4 2 0

p1(t) p2(t)

0

383

0.005 0.01 0.015 0.02 0.025 Time (s) Fig. 6. (a) Original pressure traces measured in the laboratory experiments; and (b) Pressure

384

oscillations before the first boundary reflection (Values adjusted according to scaling

385

procedures in Section 4.2).

386

The incident waves and the wave reflections are then time-windowed as outlined previously as

387

step 1 in the analysis methodology. The measured incident waves are used to determine the

388

empirical transfer function H ( s) using Eq. (14) in Step 3. The amplitude spectrums of the

389

measured wave reflections are checked to investigate the effective frequency range (the

390

bandwidth) as depicted in Fig. 7. It is found that most energy of the reflected signals is in the


frequencies less than 300 Hz. Given this, a cut-off frequency at 600 Hz is selected to avoid

392

effects of noise in the high frequency range but also to cover the effective bandwidth of the

393

reflected waves.

Magnitude

391

250

p1r(t)

200

p2r(t)

150 100 50 0

0

394

200 400 600 Frenquency (Hz)

800

395

Fig. 7. Amplitude spectrum of the reflected waves.

396

The positive and negative traveling pressure reflection waves p1r (t ) (propagating towards the

397

closed in-line valve) and p1r (t ) (propagating towards the tank) are determined by Eqs. (21) and

398

(22) for frequencies up to 600 Hz in Step 4. The results are given in Fig. 8 and compared with

399

the predicted results generated by MOC simulations (the procedure is the same as that used in

400

the numerical study, i.e. only deterioration on one side is considered when generating the

401

predicted results).


402

(a)

0

Head (m)

-0.2 -0.4 -0.6 -0.8

p1r+(t)

-1

Predicted positive reflection

0

0.005 0.01 0.015 0.02 Time (s)

0.025

(b)

0.1 0

Head (m)

-0.1 -0.2 -0.3 -0.4 -0.5

p1r-(t)

-0.6

Predicted negative reflection 0

0.005

0.01 0.015 Time (s)

0.02

0.025

403

Fig. 8. (a) Directional reflected pressure waves traveling towards the closed in-line valve; and

404

(b) Directional reflected pressure waves traveling towards the tank.

405

It can be seen that in the directional waves, reflections from the two thinner-walled sections

406

are separated, and the determined directional wave reflections are consistent with the


407

numerically generated predicted results. The superimposed reflection is reconstructed by

408

adding p A (t ) and p A (t ) together and then comparing them with the original measured wave

409

reflection p1r (t ) in Fig. 9. The reconstructed reflection trace is generally consistent with the

410

original measured reflection trace, with small differences due to the exclusion of the frequency

411

components above 600 Hz in the wave separation. Overall, the experimental results have

412

illustrated the feasibility of the separation of directional traveling pressure waves in pipelines

413

using dual-sensors.

Head (m)

0

-0.5

-1 p1r(t) p+1r(t) + p-1r(t)

-1.5 0 414

0.005 0.01 0.015 0.02 0.025 Time (s)

415

Fig. 9. Comparison between the original wave reflections measured at T1 (the solid line) and

416

the superimposed result of the determined directional wave reflections (the dashed line).

417

Application to pipeline condition assessment

418

The time domain condition assessment technique as outlined in (Gong et al. 2013) is how

419

applied to the resultant directional reflection waves [ p1r (t ) and p1r (t ) as shown in Fig. 8] to


420

determine the wall thickness of the thinner-walled sections (the Class B and C sections). It is

421

known that the external diameter of the experimental pipeline is uniform and the change in

422

class affects the internal diameter. For this scenario, the relationship between the relative size

423

of a wave reflection and the relative change in the wall thickness is derived as (Gong et al.

424

2013)

K E  a02c1   ( K /  )(1  erc )   1  2erc K /   erc a02 K /   a02   2 K E  a02c1   ( K /  )(1  erc )   1  2erc K /   erc a02 K /   a02   2

pn 

425

(23)

426

where pn represents the normalized head perturbation of the reflected wave and is defined as

427

pn   pr  pi  pi , where pr and pi

428

respectively ; erc is the relative change in wall thickness and is defined as erc   ed  e0  e0 ,

429

where e0 and ed represent the wall thickness in the intact and deteriorated section respectively;

430

a0 is the wave speed in the intact pipe.

are the sizes of reflected wave and incident wave

Normalized reflection, pn

0

431

-0.02 -0.04 -0.06 -0.08 -0.1

a0 = 1319 m/s

-0.12 -0.5 -0.4 -0.3 -0.2 -0.1 0 Relative change in wall thickness, erc


432

Fig. 10. Relationship between the normalized wave reflection ( pn ) and the relative change in

433

the wall thickness ( erc ) for the experimental pipeline.

434

The plot of Eq. (23) is given in Fig. 10. The theoretical wave speed in the intact (Class A) pipe

435

is considered, which is a0  1319 m/s as in Table 2. The range of erc used is from erc = – 0.5

436

to erc = 0, which represents wall thickness variation from half the original wall thickness to the

437

original wall thickness. The plot can serve as a look-up chart for condition assessment for pipes

438

with internal changes in wall thickness.

439

It is obvious that the original pressure measurements as shown in Fig. 9 cannot be directly used

440

for condition assessment because the reflections from the Class B and the Class C sections are

441

superimposed. In contrast, the separated directional wave reflections as shown in Fig. 8 show

442

the wave reflections from the two sections separately and clearly, and they can easily be used

443

for further analysis.

444

The values of the relative wave reflections ( pr  pi ) from the Class C and Class B sections

445

are determined from the minima of p1r (t ) and p1r (t ) respectively as shown in Fig. 8, for which

446

the results are p1r  pi = – 0.64 m and p1r  pi = – 0.40 m respectively. The magnitude of the

447

incident step wave is determined as pi = 6.60 m from the measured trace shown in Fig. 6(b).

448

As a result, the normalized reflections for the Class C and Class B sections are pn = – 0.097

449

and pn = – 0.061, respectively. Referring to the look-up chart in Fig. 10, the relative change

450

in wall thickness corresponding to these two wave reflections are erc = – 0.44 and erc = – 0.29,

451

respectively. Finally, using the wall thickness of the Class A pipe of e0 = 1.63 mm, the wall

452

thicknesses in the Class C and Class B sections are determined by the reflection analysis as e 


453

= 0.91 mm and e  = 1.16 mm, respectively. Compared with the wall thicknesses as given by

454

the manufacturer ( e2 = 0.92 mm and e1 = 1.22 mm as shown in Table 2), the wall thicknesses

455

are estimated with relatively high accuracy.

456

These results have demonstrated that the wave separation algorithm as developed in this

457

research can significantly facilitate pipeline condition assessment by resolving the complexity

458

due to wave superposition.

459

Conclusion

460

A wave separation algorithm has been developed for extracting the directional hydraulic

461

transient pressure waves that travel along a pipeline in the downstream and upstream directions,

462

respectively. Discrete incident transient waves, such as a single pulse or a step wave that are

463

commonly used in transient-based pipeline fault detection, are used to excite a pipeline system

464

and induce reflections from deteriorated pipe sections. The wave separation is achieved by

465

analysing the pressure responses of the pipeline as measured by a proximity dual-sensor setup.

466

The wave separation resolves the complexity of the superposition of traveling pressure waves

467

in a pipeline, providing directional information of wave reflections and simplifying the wave

468

forms. The key contributions of the research include: (1) the development of an empirical

469

technique for estimating the transfer function between two sensors that is more practical than

470

analytical estimation for real pipelines with parameter uncertainties; (2) the further

471

development of the conventional wave separation algorithm to enhance the accuracy for the

472

separation of the relatively small wave reflections by removing the dependence of the relatively


473

large incident wave; and (3) the verification of the wave separation technique by numerical and

474

laboratory experiments.

475

In the numerical simulations, a discrete pulse pressure wave is considered as the incident wave,

476

which has not been studied previously for hydraulic transient wave separation in pipelines.

477

Three thinner-walled pipe sections are placed in the numerical pipeline system, with two of

478

them simulating deteriorated sections due to internal corrosion and one simulating a section

479

with a lower pipe class. The wave separation algorithm has been successfully implemented,

480

with the resultant directional reflection waves consistent with the predicted results.

481

Experimental verification of the hydraulic transient wave separation algorithm has been

482

conducted. A step transient pressure wave generated by a fast closure of a side-discharge valve

483

is considered as the incident wave. The original pressure responses as measured by the dual-

484

sensors spaced at 0.99 m include the superimposed wave reflections from two thinner-walled

485

pipe sections. The directional reflection waves are extracted by the wave separation algorithm

486

and the results are generally consistent with the numerically generated predicted results. An

487

existing pipeline condition assessment technique that is based on direct time domain analysis

488

of wave reflections is adopted and applied to the extracted directional waves. The wall

489

thicknesses of the two thinner-walled pipe sections are estimated from the reflected waves and

490

the results are consistent with the specifications provided by the manufacturer. The

491

experimental study has validated the proposed wave separation algorithm, and confirmed the

492

usefulness of the algorithm in transient-based pipeline condition assessment and fault detection.

493

494

Acknowledgements


495

The research presented in this paper has been supported by the Australia Research Council

496

through the Discovery Project Grant DP140100994 and the Linkage Project Grant

497

LP130100567.

498

Notations

499

The following symbols are used in this paper: A

=

cross sectional area of pipe (m2);

a

=

wave speed (m/s);

C

=

pipeline compliance operator (s-1);

c1

=

pipeline restraint condition coefficient (-);

D

=

internal diameter of pipeline (m);

E

=

Young’s modulus of pipe material (Pa);

e

=

pipe wall thickness (m);

erc

=

relative change in wall thickness (-);

f

=

Darcy-Weisbach friction factor (-);

H

=

transfer function of a pipeline (-);

K

=

bulk modulus of elasticity of fluid (Pa);

l

=

distance between two sensors (m);


Px

=

frequency domain representation of pressure waves at location x (m);

Px 

=

frequency domain representation of positive traveling pressure wave at location x (m);

Px 

=

frequency domain representation of negative traveling pressure wave at location x (m);

500

pn

=

normalized head perturbation of reflected wave (-);

px

=

time domain pressure signal measured at location x (m);

px 

=

time domain positive traveling pressure wave at location x (m);

pxr 

=

time domain positive traveling reflected pressure wave at location x (m);

px 

=

time domain negative traveling pressure wave at location x (m);

pxr 

=

time domain negative traveling reflected pressure wave at location x (m);

Q

=

steady-state flow (m3s-1);

R

=

resistance term (s-1);

s

=

Laplace variable (-);

t

=

time (s);

x

=

distance along the pipe (m);


501

Greek symbols: 

=

fluid line propagation operator (m-1);



=

density of fluid (kgm-3);



=

angular frequency (rad).

502

503

References

504

Chaudhry M. H. 2014 Applied Hydraulic Transients. Springer, New York, NY.

505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530

Chung J. Y. & Blaser D. A. 1980 Transfer function method of measuring in‐duct acoustic properties. I. Theory. The Journal of the Acoustical Society of America 68(3), 907-13, 10.1121/1.384778. Colombo A. F. & Karney B. W. 2002 Energy and costs of leaky pipes toward comprehensive picture. Journal of Water Resources Planning and Management 128(6), 441-50. Covas D., Ramos H. & De Almeida A. B. 2005 Standing wave difference method for leak detection in pipeline systems. Journal of Hydraulic Engineering 131(12), 1106-16, 10.1061/(ASCE)0733-9429(2005)131:12(1106). Duan H.-F. 2016 Transient frequency response based leak detection in water supply pipeline systems with branched and looped junctions. Journal of Hydroinformatics, 10.2166/hydro.2016.008. Ferrante M. & Brunone B. 2003 Pipe system diagnosis and leak detection by unsteady-state tests. 1. harmonic analysis. Advances in Water Resources 26(1), 95-105. Ferrante M., Massari C., Todini E., Brunone B. & Meniconi S. 2013 Experimental investigation of leak hydraulics. Journal of Hydroinformatics 15(3), 666-75, 10.2166/hydro.2012.034. Gong J., Zecchin A. C., Lambert M. F. & Simpson A. R. 2012a Signal separation for transient wave reflections in single pipelines using inverse filters. In: World Environmental and Water Resources Congress 2012: Crossing Boundaries, ASCE, Albuquerque, New Mexico, United States, pp. 3275-84. Gong J., Lambert M. F., Simpson A. R. & Zecchin A. C. 2012b Distributed deterioration detection in single pipelines using transient measurements from pressure transducer pairs. In: 11th International Conference on Pressure Surges Anderson S (ed.), BHR Group, Lisbon, Portugal, pp. 127-40. Gong J., Simpson A. R., Lambert M. F., Zecchin A. C., Kim Y. & Tijsseling A. S. 2013 Detection of distributed deterioration in single pipes using transient reflections.


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Journal of Pipeline Systems Engineering and Practice 4(1), 32-40, 10.1061/(ASCE)PS.1949-1204.0000111. Gong J., Lambert M. F., Simpson A. R. & Zecchin A. C. 2014 Detection of localized deterioration distributed along single pipelines by reconstructive MOC analysis. Journal of Hydraulic Engineering 140(2), 190-8, DOI: 10.1061/(ASCE)HY.19437900.0000806. Gong J., Lambert M. F., Zecchin A. C., Simpson A. R., Arbon N. S. & Kim Y.-i. 2016 Field study on non-invasive and non-destructive condition assessment for asbestos cement pipelines by time-domain fluid transient analysis. Structural Health Monitoring 15(1), 113-24, 10.1177/1475921715624505. Karim M. R., Abbaszadegan M. & Lechevallier M. 2003 Potential for pathogen intrusion during pressure transients. Journal of American Water Works Association 95(5), 13446. Lee P. J., Vítkovský J. P., Lambert M. F., Simpson A. R. & Liggett J. A. 2005 Frequency domain analysis for detecting pipeline leaks. Journal of Hydraulic Engineering 131(7), 596-604, 10.1061/(ASCE)0733-9429(2005)131:7(596). Ljung L. 1999 System Identification - Theory for the User. Prentice-Hall, Inc., Upper Saddle River, New Jersey. Massari C., Yeh T. C. J., Ferrante M., Brunone B. & Meniconi S. 2014 Detection and sizing of extended partial blockages in pipelines by means of a stochastic successive linear estimator. Journal of Hydroinformatics 16(2), 248-58, 10.2166/hydro.2013.172. Meniconi S., Duan H. F., Lee P. J., Brunone B., Ghidaoui M. S. & Ferrante M. 2013 Experimental investigation of coupled frequency and time-domain transient test-based techniques for partial blockage detection in pipelines. Journal of Hydraulic Engineering 139(10), 1033-44. Mpesha W., Gassman S. L. & Chaudhry M. H. 2001 Leak detection in pipes by frequency response method. Journal of Hydraulic Engineering 127(2), 134-47, 10.1061/(ASCE)0733-9429(2001)127:2(134). Sattar A. M., Chaudhry M. H. & Kassem A. A. 2008 Partial blockage detection in pipelines by frequency response method. Journal of Hydraulic Engineering 134(1), 76-89, 10.1061/(ASCE)0733-9429(2008)134:1(76). Soares A. K., Covas D. I. C. & Reis L. F. R. 2011 Leak detection by inverse transient analysis in an experimental PVC pipe system. Journal of Hydroinformatics 13(2), 153-66, 10.2166/hydro.2010.012. Stephens M. L., Lambert M. F. & Simpson A. R. 2013 Determining the internal wall condition of a water pipeline in the field using an inverse transient model. Journal of Hydraulic Engineering 139(3), 310–24, 10.1061/(ASCE)HY.1943-7900.0000665. Wylie E. B. & Streeter V. L. 1993 Fluid Transients in Systems. Prentice Hall Inc., Englewood Cliffs, New Jersey, USA. Zecchin A., Lambert M., Simpson A. & White L. 2014a Parameter identification in pipeline networks: transient-based expectation-maximization approach for systems containing unknown boundary conditions. Journal of Hydraulic Engineering 140(6), 04014020, 10.1061/(ASCE)HY.1943-7900.0000849. Zecchin A. C. 2009 Laplace-domain analysis of fluid line networks with application to timedomain simulation and system parameter identification. PhD Dissertation, School of Civil, Environmental and Mining Engineering, The University of Adelaide, Adelaide.


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Zecchin A. C., White L. B., Lambert M. F. & Simpson A. R. 2013 Parameter identification of fluid line networks by frequency-domain maximum likelihood estimation. Mechanical Systems and Signal Processing 37(1-2), 370-87, 10.1016/j.ymssp.2013.01.003. Zecchin A. C., Gong J., Simpson A. R. & Lambert M. F. 2014b Condition Assessment in Hydraulically Noisy Pipeline Systems Using a Pressure Wave Splitting Method. Procedia Engineering 89, 1336-42, 10.1016/j.proeng.2014.11.452.

Hydraulic Transient Wave Separation Algorithm using

Hydraulic Transient Wave Separation Algorithm using

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