a longitudinal study of vibration-based water flow sensing

8

A Longitudinal Study of Vibration-Based Water Flow Sensing

YOUNGHUN KIM, IBM T. J. Watson ResearchHEEMIN PARK, Sookmyung Women’s UniversityMANI B. SRIVASTAVA, University of California, Los Angeles

We present a long-term and cross-sectional study of a vibration-based water flow rate monitoring systemin practical environments and scenarios. In our earlier research, we proved that a water flow monitoringsystem with vibration sensors is feasible by deploying and evaluating it in a small-scale laboratory setting.To validate the proposed system, the system was deployed in existing environments—two houses and apublic restroom—and in two different laboratory test settings. With the collected data, we first demonstratevarious aspects of the system’s performance, including sensing stability, sensor node lifetime, the stabilityof autonomous sensor calibration, time to adaptation, and deployment complexity. We then discuss thepractical challenges and lessons from the full-scale deployments. The evaluation results show that our watermonitoring solution is a practical, quick-to-deploy system with a less than 5% average flow estimation error.

Categories and Subject Descriptors: H.4.m [Information Systems Applications]: Miscellaneous

General Terms: Algorithms, Design, Experimentation, Measurement, Performance

Additional Key Words and Phrases: Application of sensor networks, adaptive sensor calibration, nonintrusiveand spatially distributed sensing, parameter estimation via numerical optimization

ACM Reference Format:Kim, Y, Park, H., and Srivastava, M. B. 2012. A longitudinal study of vibration-based water flow sensing.ACM Trans. Sensor Netw. 9, 1, Article 8 (November 2012), 28 pages.DOI = 10.1145/2379799.2379807 http://doi.acm.org/10.1145/2379799.2379807

1. INTRODUCTION

The U.S. Environmental Protection Agency states that 3 trillion gallons of water couldbe saved each year if every household in the U.S. decreased its water consumption by30 percent.1 Such a decrease would result in a dollar-volume saving of $49.3 millionper day or more than $18 billion a year. Water conservation is of even greater financialsignificance because rising purification costs are being compounded by rapid demand

1U.S. Environmental Protection Agency. Watersense. http://epa.gov/watersense/index.htm.

Part of this work is based on Kim, Y., Schmid, T., Charbiwala, Z. M., Friedman, J., and Srivastava, M. B. 2008.NAWMS: Nonintrusive autonomous water monitoring system. In Proceedings of the 6th ACM Conference onEmbedded Networked Sensor Systems.This material is supported in part by the NSF under award CNS-0820061, CNS-0905580, and CNS-1143667,and by the Center for Embedded Networked Sensing at UCLA. Any opinions, findings and conclusions orrecommendations expressed in this material are those of the authors and do not necessarily reflect the viewsof the listed funding agencies.Authors’ addresses: Y. Kim, Services for a Smarter Planet, IBM T. J. Watson Research, Hawthorne, NY;email: [email protected]; H. Park, Department of Multimedia Science, Sookmyung Women’s University,Seoul, South Korea; M. B. Srivastava, Electrical Engineering Department and Computer Science Depart-ment, University of California, Los Angeles, CA.Permission to make digital or hard copies of part or all of this work for personal or classroom use is grantedwithout fee provided that copies are not made or distributed for profit or commercial advantage and thatcopies show this notice on the first page or initial screen of a display along with the full citation. Copyrights forcomponents of this work owned by others than ACM must be honored. Abstracting with credit is permitted.To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of thiswork in other works requires prior specific permission and/or a fee. Permissions may be requested fromPublications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212)869-0481, or [email protected]© 2012 ACM 1550-4859/2012/11-ART8 $15.00

DOI 10.1145/2379799.2379807 http://doi.acm.org/10.1145/2379799.2379807

ACM Transactions on Sensor Networks, Vol. 9, No. 1, Article 8, Publication date: November 2012.

8:2 Y. Kim et al.

growth. American public water supply and treatment facilities consume about 56 billionkWh per year (enough electricity to power over 5 million homes1). To make mattersworse, higher global temperatures are affecting our fresh water reserves in ice andsnow caps. The Water Poverty Index [Center for Ecology & Hydrology 2005] illustratesthat an urgent global initiative toward conservation is necessary.

In addition, domestic hot water usage accounts for up to 30 percent of the averagehome’s energy budget [World Business Council for Sustainable Development 2009].Therefore, the ability to measure hot water usage by endpoints is critical for helpingconsumers to understand the implications of energy use and make informed decisions.

As the literature on domestic energy conservation shows [McMakin et al. 2002;Stern 1999; Froehlich et al. 2009], a fundamental component of sustainable homes isa low-level system that profiles fine-grained resource consumption measurement at areasonable cost. In addition, a report by the World Business Council for Sustainable De-velopment (WBCSD) [2008] states that due to a “lack of awareness and information onenergy consumption and cost, people are often not aware that they are wasting energy,which prevents them from behaving efficiently.” Studies by McMakin et al. [2002] haveidentified that continued awareness is as important for producing sustained changes inhuman behaviors that affect energy conservation as are incentives and disincentives.The WBCSD [2008] also notes that “Technical devices to measure energy consump-tion and provide immediate feedback help households to cut energy consumption byas much as 20%. Direct and immediate feedback reveals the link between actions andtheir impacts. Well-informed consumers choose actions to save energy with minimalimpact on their comfort.”

The same principles apply to domestic water conservation. However, fine-grainedwater flow monitoring in built environments is considered costly. For example, cur-rent consumer-grade water flow meters are meant to be installed in-line, requiringnon-trivial plumbing that is best handled by a professional. Therefore, the conven-tional means of obtaining high-resolution data would come with high installation andmaintenance costs due to an increased number of possible water leak points.

In addition, main water flow information alone is not sufficient to pinpoint wastefulwater-consuming activities unless meaningful disaggregated measures are provided[Froehlich et al. 2009; Chen et al. 2011].

In Kim et al. [2008], we proposed and evaluated a less-intrusive water flow moni-toring system in a laboratory setting. In the proposed solution, we demonstrated theproof-of-concept design of an economical tool for pipe-level water flow monitoring. Whileits feasibility was shown, several questions had not been fully answered: (1) how welldoes the vibration-based water flow rate estimation perform in realistic environments;(2) how well does the sensing system scale; (3) how well does it work with differentpipes composed of various materials under various installation settings; and (4) doesthe system achieve long-term stability both in estimation and system performance?

To answer these questions, we present a long-term and cross-sectional study of theproposed solution in built environments. We deployed vibration-based water flow mon-itoring systems in various settings, including laboratory test beds, a public restroom,and two houses with increased deployment complexity. With the collected data, wefirst demonstrate various aspects of the system’s performance, such as estimation ac-curacy across various pipe sizes, materials, and different sensor placements, flow ratetracking performance with compound water-consuming events, sensing stability, andlong-term accuracy and performance changes. We then discuss the findings from ourexperiments, such as node lifetime, stability of the autonomous sensor calibration,time to installation, and deployment complexity. Finally, we present the practical chal-lenges and lessons from the full-scale deployment. The evaluation results prove that thevibration-based water flow rate estimation system can be a practical, quick-to-deploy


A Longitudinal Study of Vibration-Based Water Flow Sensing 8:3

system that exhibits less than 5% average error for residents who want to understandtheir daily water usage in buildings.

The contributions of this article are three-fold. (1) We completely redesigned thesensing platform to achieve better dynamic range and battery life. As noted in Kimet al. 2008], the previous prototype had limited battery life and limited accuracy in lowflows due to the limited ADC resolution. To reduce the power consumption, we useda more energy-efficient acceleration sensor. The previous prototype could run 14 to 20days with continuous sampling; our new design can operate 270 days to 350 days withonly two AA batteries (or 2 to 5 years with a lower sampling rate). We evaluated theestimation performance of the improved platform in various deployment scenarios andshowed that vibration-based flow estimation in built environments is feasible. (2) Weconducted a long-term (up to 45 days) and cross-sectional evaluation (up to ten pipes be-ing simultaneously monitored) of the proposed solution in several built environments.With substantially more evaluation data, we present thorough evaluations of the pro-posed solution for various pipe types, materials, and sizes in a public restroom, twohouses, and laboratory test beds. (3) Finally, we discuss our findings, lessons, and expe-rience. In addition to the performance results, we describe pipe crosstalk, sensitivity toexternal noise sources, observed battery drain characteristics, and water-consumptiontrends and their implications.

This article is organized as follows. This article briefly reviews emerging resourcemonitoring technologies. In particular, we highlight a pressure-based water event mon-itoring system [Froehlich et al. 2011; Froehlich et al. 2009], a self-powered miniatureinline water flow meter [Gupta et al. 2010], and a mobile pipe monitoring sensor nodefor discovering pipe topology [Lai et al. 2010], and we describe the differences betweenour vibration-based flow monitoring system and these technologies. We then presentthe background for the vibration-based water flow estimation method and its methodof automatic calibration. In Section 4, we describe the improved vibration flow estima-tion sensor node and deployment scenarios. In Section 6, we discuss findings, practicalissues, and remedies gathered from the deployments.

2. RELATED WORK

In recent years, a series of solutions for residential resource monitoring have beenproposed [Froehlich et al. 2011; Froehlich et al. 2009; Fogarty et al. 2006; Stoianovet al. 2007; Lai et al. 2010; Kim et al. 2008; Campbell et al. 2010; Jiang et al. 2009;Patel et al. 2007; Gupta et al. 2010]. Solutions span appliance-level power monitoring[Kim et al. 2009, 2008; Jiang et al. 2009; Patel et al. 2007], gas monitoring [Cohn etal. 2010], and water monitoring [Froehlich et al. 2011; Froehlich et al. 2009; Fogartyet al. 2006; Stoianov et al. 2007; Lai et al. 2010; Kim et al. 2008; Campbell et al. 2010].The goal of these emerging technologies is to furnish residents with an economical wayof understanding their resource-consumption patterns at a finer level of granularity.While each technology has its own benefits and limitations, we focus on reviewing thework related to domestic water flow monitoring.

A conventional method for deriving high-resolution data is to install inline waterflow sensors. Unfortunately, not all water-consuming endpoints have faucet ends (e.g.,a toilet bin, a sprinkler system, a laundry machine, a dishwasher). The inline sensorcannot monitor water consumption from the endpoints that do not have faucet endswithout performing plumbing work. Moreover, some faucets are often connected to bothhot- and cold-water pipes. Therefore, the conventional method has a limitation: it lacksthe ability to break down the total consumption into its hot- and cold-water componentsunless the inline sensor is separately installed in both the hot- and cold-water pipes.By contrast, our system can be attached to the surface of the hot and cold pipes underthe sink. In the evaluation section, we demonstrate the breakdown and estimation


8:4 Y. Kim et al.

accuracy for hot- and cold-water consumption in a public restroom and two residentialbuildings.

Froehlich et al. [2009] have proposed a single-point sensing approach (also known asinfrastructure mediated sensing) that can detect the on and off events of various wa-ter fixtures in residential spaces. They found that there are unique transient pressurechanges in water pipe networks for each fixture. The key benefit of this approach is thatit requires only one or two pressure sensors to monitor the water-consuming activitiesof an entire house. Froehlich et al. [2011] showed that it is possible to detect water-related activities with high accuracy in single-family houses with isolated plumbingsystems. However, this approach is not free of limitations. For example, they foundthat the detection accuracy degrades in apartment units where multiple units sharecomplex pipe networks. In addition, this approach requires an explicit training phaseduring which users need to turn on and off their most-used water fixtures. Their systemis different from ours in two ways. (1) The single-point sensing approach focuses on de-tecting unique water-consuming activities, whereas our system focuses on monitoringthe real-time water flow of each individual pipe. (2) Their system requires an explicittraining phase to determine the unique signatures of water activities. Our approachuses an automatic calibration method that does not require manual system training.

To improve the lifetime of the single-point sensing approach [Froehlich et al. 2009],Campbell et al. [2010] have developed a small device for harvesting energy from waterpressure that can be installed at any faucet end. This small form factor allows residentsto monitor faucet-level water consumption activities. They demonstrated the system’sapplicability to the system in Froehlich et al. [2009].

Lai et al. [2010] have developed a miniaturized mobile sensor system that can deter-mine the spatial topology of hidden pipes behind walls (a droplet-type wireless sensornode equipped with pressure and gyro sensors). By monitoring the pressure changesand angular movements of the mobile sensor node, the system determines the locationtrace while moving inside the pipe network. They showed that the accuracy of the esti-mated three-dimensional pipe topologies averages about 15 for 335-cm pipe networks.While they focused on determining the spatial map of the hidden pipe topologies, wefocus on estimating the water flow rate of individual pipes. Their work, however, canbe used first to determine pipe topologies, which can help us deploy our system. In thismanner, the two systems complement each other.

Chen et al. [2011] described an unsupervised learning method that identifies uniquewater-consuming activities using smart water meter data from Dubuque, Iowa. Theyshowed that it is possible to identify water-consuming activities from coarse-grainedmeter readings that are sampled every 15 minutes. The reported recall of toilet eventsis as high as 89%. While their approach can be used to associate water consumptionwith activities such as showering, doing laundry, and so forth, it lacks the abilityto disambiguate compound events that constitute up to 22% of total water-consumingactivities [Froehlich et al. 2009]. Our system, by contrast, is designed to track real-timewater-consumption rates when water flows through several pipes in a time-varyingfashion.

3. BACKGROUND

For completeness, we briefly describe our earlier research on the non-intrusive waterflow monitoring proposed in Kim et al. [2008].

3.1. Vibration to Water Flow Model

When water flows in a pipe, many molecules collide against the pipe wall (see Figure 1).According to the first law of thermodynamics, some part of this kinetic energy convertsto heat as the turbulent eddies dissipate, but most of it translates into potential energy



Fig. 1. Microscopic view of water flow in a pipe.

in the form of pressure [Pittard and Blotter 2003]. The pipe, in turn, deforms con-verting potential to kinetic (during deformation) and back to potential, as deformationcompletes. The elasticity of the pipe material applies a restoring force. Evans et al.[2004] show that vibration in a pipe results from this energy conversion cycle and isproportional to the average flow rate within the pipe.

Evans et al. decomposed the velocity of a fluid at a point in the pipe into the time-average velocity(u, v) and fluctuating velocity(u′, v′). Although there is no net flow inthe perpendicular direction to the pipe axis, the time-averaged velocity in that directionv is zero, and the time average of their product u′ · v′ is, in general, negative.

From a non-trivial derivation by Evans et al., we have the following.

∂2y∂t2 = −CEI

∂4y∂x4 = −Cp′(x), (1)

where C = gAγ

; A is the cross sectional area of the beam; γ is the specific weight of thebeam; g is the gravity; and EI is the flexural rigidity.

This indicates that the transverse acceleration of the pipe is proportional to thepressure fluctuations in the fluid.

The principle of operation is based on the relationship between the standard devia-tion of the pipe vibration and the mean flow rate of the fluid in the pipe. Blake [1986]stated that the generation of vibration by fluid motion involves the reaction of fluidsand solids to stresses imposed by time-varying flow. For dynamically similar flows, theratio of the flow fluctuations to the average flow is constant. Bird et al. [1960] showsthis relationship by noting that the oscillatory term is the time average of the absolutemagnitude of the oscillation given by

√m, where m = u′2. They define this as “intensity

of turbulence”, which is a measure of the magnitude of the turbulent disturbance andis given by

√m

u .From the definition of turbulent flow, the intensity of turbulence expression is re-

arranged as

mu2 =

1n

∑ni=1[ui(t) − u]2

u2 , (2)

where u is the average velocity and u is the instantaneous velocity.Multiplying both sides by the number of points n and u2 and dividing by n−1, we get

1n − 1

n∑i=1

[ui(t) − u]2 = NCn − 1

u2 = Ku2. (3)


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Fig. 2. Measured pipe vibration for different flow rates of a 3/4′′ copper pipe and a 3/4′′ PVC pipe.

This shows that the flow fluctuations are proportional to the pressure fluctuationsand that the pressure fluctuations are proportional to the pipe vibration. It followsthat the standard deviation of the pipe vibration is proportional to the average flowrate. The end result, Equation (3), gives an important point that regardless of the pipemounting methods, shape, and topology, at any exposed point on a pipe, we can find asignal that is strongly correlated with the water flow rate at that point.

With this relation, Evans et al. [2004] used a squared root parametric model to mapfrom vibration to water flow. To improve estimation accuracy, an extended parametricmodel is chosen based on the experimental results in Kim et al. [2008],

f (t) = α3√

v(t) + β√

v(t) + γ v(t) + δ, (4)

where f (t) is the water flow rate, and v(t) the measured vibration.Equation (4) means that once calibration parameters are known, we can estimate

water flow rate based on vibration.In the evaluation section, we evaluate this empirical model by testing estimation

accuracy on various pipe sizes and pipe materials (see Figure 2).

3.2. Autonomous Vibration Sensor Calibration

The key challenge in using vibration sensors is that it is difficult to calibrate them. Weformulate an autonomous calibration problem for distributed vibration sensors.

While plumbing systems in different households differ from each other, in residentialbuildings, a main water pipe supplies water to a boiler and the rest of cold water pipes.In this network, nodes are either branching points or merging points. Merging nodestypically appear just before faucet ends or water-consuming endpoints where hot andcold water need to be mixed.

As depicted in Figure 3, a plumbing system consists of the main water meter andone vibration sensor on each of the N subpipes. The water meter provides the systemwith the real-time water flow M(t)—an accurate measurement for the main pipe. Wedenote the flow rate in each subpipe i as fi(t).

Vibration sensors are essentially placed on pipe surfaces. Assume that there’s no wa-ter leakage and that branch pipes are being monitored, the total flow rate, M(t), is equalto the sum of the flow rates of each instrumented pipe. Then we have following relation.

M(t) =n∑

i=1

fi(t), (5)

where fi(t) = αi3√

vi(t) + βi√

vi(t) + γivi(t) + δi.



Fig. 3. Simplified view of pipe networks: A general pipe topology in residential space can be seen as anetwork. In this figure, a main water pipe supplies water to a boiler and the rest of cold water pipes. Somecold- and hot-water pipes meet at faucet ends. Vibration-based sensors can be installed on the pipe surface,allowing for the monitoring of hot and cold water pipes separately.

Assume that the sensors are synchronized and that they sample the vibration every�t seconds. Thus, Equation (5) in discrete-time becomes M(k�t) = ∑n

i=1 fi(k�t). Aftercollecting K samples of M(t) every �t seconds, we get K equalities such that

M(k�t) =n∑

i=1

fi(k�t) for k = 1, 2, 3, . . ., K. (6)

We define

Mdef= [

M(�t), M(2�t), . . ., M(K�t)]T

,

Fdef=

[n∑

i=1

fi(�t),n∑

i=1

fi(2�t), . . .,n∑

i=1

fi(K�t)

]T

.

We now formulate Equation (6) as an optimization problem, because M = F holdstrue unless there is water leakage. Thus, the optimization problem is written as

min ||M − F||1subject to 0 ≤ fi(k�t) ≤ fi,max, (7)

where M(k�t) and vi(k�t) are measurements from the sensors and αi, βi, γi, and δi arethe decision variables.

The solution to the problem yields the calibration parameters for each pipe end.Thus, no human intervention is necessary to calibrate the system.

3.3. Accounting for Vibration Propagation

As noted in Kim et al. [2008], vibration from one pipe can propagate to other pipesegments. To compensate for this side effect, a first-order linear model is used.

vi(t) = pi, jv j(t), (8)

where vi(t) is the Measured vibration on pipe i; pi, j is the vibration propagation constantfrom pipe j to pipe i; and v j(t) is the water flow-induced vibration on pipe j.


8:8 Y. Kim et al.

Generalizing this to the case where the measured vibration on a pipe i is the super-position of all possible vibrations, we get the following.

vi(t) =n∑

j=1

pi, jv j(t), (9)

pi, j = 1 if i = j,0 ≤ pi, j < 1 else.

(10)

With this constraint, the update calibration problem is in the following form.

min ||M − F||1subject to 0 ≤ fi(k�t) ≤ fi,max,

vi(k�t) =n∑

j=1

pi, jv j(k�t). (11)

Equation (7) is a non-convex programming problem, which is not solvable in poly-nomial time. Two relaxed forms are derived in Kim et al. [2008]: (a) a generalizedgeometric programming (GP) problem, by relaxing and restricting the constraints withreasonably tight bounds while conserving physically meaningful values, and (b) a two-phase linear programming (LP) problem, by decomposing the optimization problem intwo parts. It is well known that both GP and the two-phase LP problems can be solvedin polynomial time [Boyd and Vandenberghe 2004; Boyd et al. 2005]. We refer [Kimet al. 2008] for further details.

For Equation (11) to yield accurate calibration parameters, sufficient sample dataneed to be provided. Note, however, that the problem is set to minimize the overall flowestimation error, which searches for a solution that gives parameters with minimal flowestimation error. This means, in practice, that even with a limited set of measurementdata, the estimated flow rate gives a good estimate. In the evaluation section, the datafrom a long-term study illustrates this case.

We choose L1-norm minimization with linear inequality constraints, since this tendsto be less sensitive to significant outliers compared to a least squares approach [Boydand Vandenberghe 2004].

3.4. Correction Mechanism and Performance Metric

By solving the optimization problems, the system can automatically estimate the cal-ibration parameters. However, system characteristics could change over time due totopological changes, seasonal temperature variations, and aging. Therefore, we need amechanism that tests the system performance and recalibrates the mapping, if neces-sary, through iteratively solving the optimization problems.

A performance metric is defined by the following.

Performancedef=

∣∣∣∣∑n

i=1 fi(t) − M(t)M(t)

∣∣∣∣, (12)

where fi(t) is the estimated flow rate in pipe i. If its value is close to 0, we know thesystem is performing well, since the sum of the estimated flow rates has to be close tothe total flow rate M(t). However, if the metric exceeds a set threshold ε, the systemneeds recalibration.

A further improvement can be made based on this observation. By normalizing eachestimated flow rate fi with the ratio of the total flow rate to the sum of all estimated



Fig. 4. Two-tier system and information architecture for fine-grained water flow monitoring.

flow rates, that is,

fi(t) = fi(t)M(t)∑ni=1 fi(t)

, (13)

we ensure that∑N

i=1 fi = M(t) and is nearer the real flow rate in the pipe.

4. SYSTEM DESIGN AND DEPLOYMENT SCENARIOS

4.1. System Architecture

The proposed algorithm is implemented as a two-tiered information architecture thatconsists of one accurate precalibrated sensor that provides the total sum of all flowsand uncalibrated vibration sensors for each individual pipe (Figure 4).

Thus, this architecture has three characteristics.

—The first tier is reliable, and the service provider maintains it. A user does not haveto worry about its accuracy or correct operation.

—The calibration of the non-intrusive, vibration-based water flow sensors can be auto-mated by considering the correlation between the first- and second-tier informationsources.

—The first tier is ‘ground truth’, which makes it always available. This property allowsthe system to compute and adapt the calibration parameters continuously.

For the first-tier flow sensor, there are several commercially available products(Kent/AMCO,2 American Water Works Association (AWWA),3 Automatic Meter Read-ing Association (AMRA)4) that allow for interrogating the main water meter in realtime. Various types of pulsers2 provide a pulse train that is proportional to the pipe

2Kent/AMCO. Industrial pulsers for c700. http://jerman.com/kmmeters.html.3American Water Works Association. 2005. C706-96(r05): Awwa standard for direct-reading remote-registration systems for cold-water meters.4Automatic Meter Reading Association. http://www.amra-intl.org/.


8:10 Y. Kim et al.

Fig. 5. Shenitech STUF-200H handheld water meter is used to monitor the main water pipe. A telosB witha custom-built accelerometer board is used for monitoring individual pipes.

water flow rate. An advanced water infrastructure can also be used if the water util-ities provide real-time meter readings to the end-consumers [Chen et al. 2011]. TheAutomatic Meter Reading Association (AMRA) and the American Water Works Asso-ciation (AWWA) have developed an advanced water-metering infrastructure in whichwater meters transmit real-time meter information wirelessly for billing purposes.This infrastructure is already available in Germany,5 the U.K., (SmartMeter),6 theU.S. [Chen et al. 2011], and elsewhere.

For the second-tier vibration sensor nodes, sensor network nodes equipped with anaccelerometer are used to capture the signal, because the variance of the measuredaccelerations is the same as the measure of vibrations. Estimating the variance iscomputationally simple and thus can be done locally by each node. This approachresults in low communication loads.

The data collected by the vibration sensors are sent to the fusion center, where thesamples and the readings from the main meter are fused to solve the automatic cali-bration problem. The solution calculates the calibration parameters for the individualvibration sensors, which can then be used to map the real-time flow in each pipe.

We use the CVX toolbox [Dahl and Vandenberghe 2011; Boyd et al. 2005], an open-source convex optimization tool, to solve the calibration problems.

4.2. System Components

The monitoring system consists of four components: a main water flow sensor, wire-less vibration sensors, relay nodes, and a base station laptop for data collection andbackground data processing (see Figure 5 for the sensing platforms).

4.2.1. Tapping into Main Water Pipe. The main water meter provides an accurate measureof the water flow rate for an entire household. We used a Shenitech STUF-200H ultra-sonic water flow meter to monitor the main water pipe (Figure 5(a)). The STUF-200His a light-weight, portable water flow meter that weighs about 540 g. Its accuracy is±1% with ±0.5% linearity in its operational range. The sensor unit was connected tothe base station by a RS-232 cable with custom data logger software. The base stationsampled the water flow rate at 1 Hz.

5EnBW Energie Baden-Wurttemberg AG. Der intelligente stromzahler. http://www.enbw.com/.6http://www.smartmeter.co.uk/.



Monitoring the main water meter, however, is not limited to the use of this particularmonitoring device. For example, another approach has been described by Cheung etal. [2005]. His technique uses a hall-effect sensor that picks up a varying magneticfield produced by a spinning collector unit on the main water meter. He reports vol-ume measurements with a resolution of 0.01892 L. Although water pipes are oftenburied underground, the meters are accessible for billing and maintenance purposesin dedicated housings.

Fortunately, a better solution is expected in the near future. The Automatic MeterReading Association4 and the American Water Works Association3 are developing asystem that relays real-time meter information wirelessly for billing purposes.7

4.2.2. Spatially Distributed Vibration-Based Water Flow Rate Sensors. The wireless vibrationsensors were implemented using telosB motes with a custom acceleration sensor board(Hitachi Metals H34), which improved the node lifetime and accuracy over the platformused in previous work [Kim et al. 2008] (Figure 5(b)). Hitachi Metals H34C is a three-axis accelerometer weighing ±3g. The telosB’s 12-bit ADC resolution offers greatersensitivity in low-flow settings; thus, we could improve the flow estimation’s dynamicrange [Kim et al. 2008]. In addition, the H34C consumes only 0.36 mA in operationmode and 1 uA in standby mode (40% more efficient in operation and 25 times moreefficient in standby than the platform used in Kim et al. [2008]).

To further maximize the node’s lifetime, we designed the distributed vibration sen-sors to be as simple as possible, following the idea of disentangling networking burdensfrom sensing nodes [Schmid et al. 2010]. We leveraged the typical deployment scenarioof domestic water monitoring in which a building infrastructure can supply power tonodes that are responsible for relaying and multihop mesh networking; however, thesensor nodes cannot be powered in such a way.

The vibration sensors need to be battery powered for two reasons. First, the vibrationsensors are installed on pipe surfaces where water could leak. AC-powered electronicsnear water could be dangerous unless proper water proofing is provided. Second, waterpipes are usually far from AC power sources. The AC power is supplied to nodes otherthan the vibration sensors that have AC-DC adapters, such as the relay and base-station nodes, because they can be installed indoors and close to AC power outlets.The system deployment scenario thus allows sensor nodes to focus on sensing taskswhile the infrastructure node handles the networking [Schmid et al. 2010]. For eachdeployment, we will later describe detailed floor plans.

As shown in Figure 6(a), node operation begins at the start state when it waits forthe base station to initiate sampling. Once it is initialized, (1) the node samples datafrom the acceleration sensor for 0.25 s at 196 Hz with DMA enabled. This samplingtime was chosen based on experiments and provides a sufficient number of samplesfor the vibration calculation. (2) It then calculates the variance of the collected data.This process takes about 20 ms on a telosB with a 4-MHz clock speed. (3) The nodethen sends out the calculated variance via its radio, which takes approximately 17 ms(including the radio up and down time).8 (4) It then sleeps for the rest of the samplinginterval. To better capture the power consumption of the entire sensor node during itsreal operation, we measured the power consumption of a vibration sensor node (shownin Figure 5(b)) using an Agilent digital multimeter 34410A instead of using the telosBpower specification. The power consumption of each state is shown in Figure 6(a). If weset the sampling interval to one second, then the mean current consumption is about

7Water meters enabled with automatic meter reading often have coarse temporal granularity. We discussthis issue in the future work section.8After each node sends a message to the nearest relay nodes, the data flows through the multihop networksto the base station. We omit the implementation details because it is not the main scope of this article.


8:12 Y. Kim et al.

Fig. 6. Vibration sensor state diagram and node lifetime calculation.

0.617 mA. With two AA batteries (with a 4000-mAh capacity), the expected lifetime ofa node is about 270 days.

In our study, we used a one-second sampling interval to achieve the best possible wa-ter flow estimate. Water-consuming events are not fast changing in real applications,however, allowing for a slower sampling interval. Because the sampling, variance calcu-lation, and radio communication have fixed durations, the increased sampling intervalimproves the node duty cycle. As shown in Figure 6(b), we can expect the lifetime of avibration sensor to be extended to a few years. In the evaluation section, we also showthat the battery level changes during long-term deployment, confirming the estimatedlifetime in real deployments.

4.3. System Deployment Description

To deploy the monitoring system, a user first installs the vibration and main water pipesensor. Either cable ties or tape can be used to attach the vibration sensors to the pipesurfaces, as shown in Figure 8. Unlike inline flow sensors, no plumbing is necessary inthis step.

After the installation phase, the monitoring system runs autonomously. First, it col-lects the vibration and water flow rate data to obtain solutions to the optimizationproblem. After the parameters are obtained, the system can estimate the individualflow rate for each pipe. The system simultaneously calculates and tests the perfor-mance metric. If this metric exceeds a predefined threshold, ε, the system recalibratesand solves the numerical optimization problem to further tune the calibration param-eters. Figure 7 describes the steps of the algorithms used to compute the calibrationparameters and performance metric.

4.4. Deployment Scenarios and Deployment Periods

To evaluate the proposed vibration-based water flow monitoring system, we deployedthe system in four different complexity scenarios: laboratory test beds, a public re-stroom, a small-size apartment unit, and a one-story residential building. Figure 9shows the floor plans of each building. In the public restroom, we monitored four wa-ter pipes: two hot-water pipes and two cold-water pipes. In the small apartment unit,the kitchen and a bathroom were monitored. The single-family house had two fullbathrooms, one half bathroom, one kitchen, and a laundry room.



Fig. 7. Algorithm flowchart: After an initial data gathering, the system solves for calibration parameters. Inruntime, the system can monitor its own performance. If the performance is not good enough, it recalibratesitself automatically.

Fig. 8. Typical vibration sensor deployments on pipes. A sensor node can be attached to a pipe surface eitherwith a cable tie or tape.

In the laboratory test beds, we deployed the system for more than three months usingvarious settings. The public restroom system was deployed over a period of three days.In the small apartment unit, we deployed the system for two weeks. The deployment inthe single-family house lasted about 45 days. The variety of the deployment scenariosand their durations were sufficient to study the validity of the proposed system, sensingstability, node lifetime, sensor calibration, and training time.

One person without any prior plumbing training spent between 30 minutes and twohours on each deployment, depending on the deployment complexity. Although thisstudy was not intended to address formal usability, this time does suggest that thesystem deployment is simple enough to not require assistance from plumbing experts.


8:14 Y. Kim et al.

Fig. 9. Deployment floor plans for a public restroom, an apartment unit, and a single-family house. Somedetails are omitted and simplified for privacy.



Table I. Vibration to Water Flow Rate Fitting Model

Pipe Fitting Model ( f (t)) Coefficient Error (%)

Copperε

4√v(t) + α

3√v(t) + β

√v(t) + γ v(t) + δ 0.001, 0.0154, 0, 0, 0.0471 1.823

α3√v(t) + β

√v(t) + γ v(t) + δ 0.1548, 0, 0, 0.0472 1.865

β√

v(t) + γ v(t) + δ 0.1067, 0, 0.0923 2.030γ v(t) + δ 0.0478, 0.1470 2.724

PVCε

4√v(t) + α

3√v(t) + β

√v(t) + γ v(t) + δ 0, 0.0893, 0, 0, 0.0150 1.052

α3√v(t) + β

√v(t) + γ v(t) + δ 0.0896, 0, 0, 0.0160 1.058

β√

v(t) + γ v(t) + δ 0.0530, 0, 0.0520 1.282γ v(t) + δ 0.0154, 0.0884 1.892

5. EVALUATION

With the data collected from the four deployment scenarios, we evaluated variousaspects of the performance of the monitoring system. We discuss further findings inSection 6. In this study, we tested the appropriateness of the empirical model. By vary-ing the parametric models, we confirmed that a third-order model is suitable for waterflow estimation with reasonable model complexity. With the chosen parameter model,we evaluated the accuracy of the flow rate estimation for numerous pipe materialsand pipe sizes. We then evaluated the quality of the sensing modality by evaluatingthe stability of the measurements. In addition, we tested the error sensitivity of thesensor placement. We also determined the dynamic range of the vibration-based flowestimation and determined the performance for variable and compound water eventsby examining the tracking performance. Finally, we summarize the accuracy results.

5.1. Vibration to Water Flow Rate Model Validation

Equation (3) suggests that the relationship between the vibration variance and theflow rate is proportional. Because of modeling inaccuracy and sensor characteristics,the relationship is unfortunately nonlinear, as Figures 2(a) and 2(b) suggest. Using awell-fitting model is essential to minimize the estimation error. Evans et al. [2004] useda root-squared model. In Kim et al. [2008], we found that a third-order root equationcan further improve estimation accuracy.

Table I summarizes the different fitting curves, their parameters, and the fitting errorfor two different types of pipe materials. In this experiment, we collected synchronouswater flow and vibration data from five independent laboratory setting runs. For eachrun, we changed the flow rate from 0 L/s to 1.5 L/s. The duration of each run was setto 25 minutes. The number of sample points was 37,530. The total water consumed inthis experiment was approximately 27 kL.

The third-order root curve was observed to have the least fitting error for bothpipes. Higher-order root curves might fit better, but the increase in complexity (morecalibration parameters to estimate) does not justify the small gain in fitting error. Asshown in Table I, the gain in modeling accuracy is saturated in the fourth-order rootparametric model.

5.2. Cross-Sectional Accuracy Test

Using the third-order root model, we evaluated empirical model (Equation (3)) byinvestigating the flow rate estimation accuracy for the various types of pipes shown inTable II. The types of pipes included most of the conventional ones used in residentialapplications, such as copper 3/4", PVC 3/4", PVC 1", copper 1/8", threaded stainless1/4", stainless 3/4", stainless 1 3/4", plastic hose 5/8", and fine threaded stainless 1/4".

To validate the model, we installed a vibration sensor on each pipe and calibratedeach vibration sensor by running the automatic calibration. To compare the estimation


8:16 Y. Kim et al.

Table II. Empirical Model Evaluation

Pipe Type Fitting Model Coefficient Estimation Error (%)Copper 3/4" 0.36, 0.17, 0.003, 0.08 2.7PVC 3/4" 0.41, 0.08, 0.06, 0.00 3.07PVC 1" 0.07, 0.21, 0.12, 0.00 4.02Copper 1/8" 0.10, 0.01, 0.00, 0.00 3.5Threaded Stainless 1/4" 0.13, 0.00, 0.00, 0.00 2.7Stainless 3/4" 0.00, 0.00, 0.16, 0.00 1.34Stainless 1 3/4" 0.00, 0.00, 0.22, 0.00 0.41Plastic Hose 0.47, 0.024, 0.00, 0.00 2.56Fine Threaded Stainless 1 1/4" 0.00, 0.00, 0.22, 0.00 0.02Fine Threaded Stainless 2 1/4" 0.00, 0.02, 0.75, 0.05 1.57

accuracy with the true water flow, we also installed a factory-calibrated inline waterflow sensor.

The data were collected from the laboratory setting, apartment unit, single-familyhousing, and public restroom. We ran three trials for each pipe. In each trial, wechanged the flow rate from 0 L/s to the fastest that each pipe could handle (varyingfrom about 0.5 L/s to more than 2 L/s). For each pipe, we first collected data to cali-brate parameters, then the estimation accuracy is tested under varied flow rate. Thecalibration period varie from three minutes to ten minutes. The test time period variedfrom 20 minutes to 90 minutes.

Table II suggests that the empirical model is generally sufficient for capturing therelationship between vibration and water flow in various pipes. The table shows thateach pipe has different calibration parameters. In all cases, the estimation error is lessthan 5%.

5.3. Estimation Accuracy and Sensor Placement Tradeoffs

One practical implication of using vibration sensors attached to pipes is that a sensor’splacement can vary depending on the installation conditions. The vibration-based waterflow estimation functioning without careful installation is a key requirement for theproposed solution to be applicable under realistic conditions.

To study this property, we attached six vibration sensors to several different pointson a 1 1/4" stainless water pipe. Figure 10 shows the experimental setup: Node 1 ona bent stainless steel pipe segment 7 cm from a wall; Node 2 right after the first 1/2"black iron elbow; Node 3 in the middle of the 40-cm pipe segment; Node 4 on the second1/2" black iron elbow; Node 5 at the end of the 50-cm pipe segment, which is 6 cm fromthe third elbow; and Node 6 in the middle of the 20-cm pipe segment (18 cm from thebrass threaded faucet end).

The six nodes synchronously sampled vibration data, and water flow rates wereestimated using the model given in Equation (4). Table III summarizes the estimationaccuracy’s dependence on the sensor placement. For this experiment, we changed thewater flow rate from 0 L/s to 1.6 L/s (a bathtub faucet with a high-flow setting canhandle this flow rate at 80 psi). Overall, we can see that the average estimation errordoes not depend on the placement.9

From these experiments, it is clear that the proposed parametric model can be usedto estimate flow rate in various types of pipes, and they can be attached on any segmentof a pipe. In addition, the proposed system is not very sensitive to external noise andthe location of sensors.

9Note that the error in the standard deviation of Node 6 is slightly worse than that of the others because thesensor is close to the faucet end. The estimated flow rate was less stable because turbulent water flow at thefaucet end and external vibration from hands on the faucet affected its measurements.



Fig. 10. Experiment setup for accuracy and placement tradeoffs.

Table III. Estimation Accuracy and SensorPlacement (Flow rate range : 0–1.6L/s)

Sensor Placement Error (%) Error STD1 1.15 4.812 0.14 5.273 1.47 6.164 0.19 3.745 0.73 5.356 0.42 10.29

5.4. Sensing Stability Test from External Vibration

If the vibration-sensing modality suffers from external vibration sources and noisymeasurements, vibration-based water flow estimation could be an unstable sensingsolution for flow estimation. To evaluate the estimation stability, we carefully exam-ined flow estimation for five days. The total water runtime for this experiment wasapproximately three hours. Figure 11 shows the histograms for the estimation, fromwhich it is clear that the vibration-based water flow estimation is stable. We see thatthe 95 percentile of the estimation is entirely within 0.04 L/s, which is finer than theresolution of the inline water flow meter that we used to collect the ground data forcomparison. The pipe we used for the experiment was part of a six-story public build-ing where the pipe topology was much more complex. This experiment shows that theproposed parametric model can be used to estimate the flow rate for various types ofpipes and that the sensors can be attached to any pipe segment. Overall, the experi-ments show that the proposed system is not overly sensitive to external noise or sensorlocation.


8:18 Y. Kim et al.

Fig. 11. Estimated water flow rate histograms from six different sensor placements. Water flows 1.17L/s.We can see from these histograms that the vibration sensor achieves as stable as inline flow meters. Theresolution of the inline water flow meter is 0.04L/s (solid lines shown in each figure for comparison), and thewidths of the 95 percentile of each histogram is 0.017L/s, 0.013L/s, 0.029L/s, 0.03L/s, 0.018L/s, and 0.019L/s,respectively.

5.5. Tracking Performance Test

To further investigate the estimation performance under a varying flow rate, we provideexperimental data from different sites. We ran five trials for each site. For each trial, wearbitrarily changed the flow rate from 0 L/s to the fastest that each pipe could handle.



0 50 100 150 200 250 300 3500

0.05

0.1

0.15

0.2

0.25

0.3

Water Flow Rate Estimate of Pipe 1 and Pipe 2

time (s)

flow

rat

e (L

/s)

SumKitchenBathroom

0 50 100 150 200 250 300 3500

0.05

0.1

0.15

0.2

0.25

0.3

True Water Flow Rate Estimate

time (s)

flow

rat

e (L

/s)

SumKitchenBathroom

Fig. 12. Tracking performance in a 1 bed and 1 bathroom apartment.

0 20 40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25Water Flow Rate Estimate of Pipe 1 and Pipe 2

time (s)

flow

rat

e (L

/s)

SumSink 1Sink 2

0 20 40 60 80 100 120 140 160 1800

0.05

0.1

0.15

0.2

0.25True Water Flow Rate Estimate

time (s)

flow

rat

e (L

/s)

SumSink 1Sink 2

Fig. 13. Tracking performance in a campus restroom.

The duration of each trial varied from two minutes to six minutes at a 1-Hz samplingrate. Figures 12, 13, and 14 show the sample tracking performance of the vibration-based water flow estimation with varying water flow. The bottom plots represent thetrue water flow rates, and the upper plots represent the estimated flow rates. Overall,the estimated flow rates track the variable water flow rates well. Table IV summarizesthe average estimation performance when tracking the varying flow rates.

To validate the flow rate tracking performance again, we installed factory-calibratedinline flow sensors on each pipe segment.


8:20 Y. Kim et al.

Fig. 14. Tracking performance in a single-family house.

Table IV. Water Flow Tracking Performance Summary Table

Cases Mean Error (%) Standard Deviation (%)Testbed Copper 3/4" 4.24 9.68Testbed PVC 3/4" 0.68 6.72Home I Bathroom Sink 0.53 4.39Home I Kitchen Sink 0.46 5.9Campus Restroom Sink I 0.82 12.45Campus Restroom Sink II 1.14 12.8Home II Pipe I 1.37 10.9Home II Pipe II 0.41 9.88Home II Pipe III 2.56 6.69

Figure 15 shows an example of the estimation accuracy in a 3/4" stainless pipe. Theupper plot shows that the estimated flow rate is linear. The estimation error is within3%.

5.6. Flow Rate Estimation Accuracy Summary

To summarize the performance with various settings, we briefly discuss the dependenceof the estimation accuracy on the type of pipe used. Table V describes the estimationaccuracy of all the prior trials. This table was constructed using the data collected fromall of the deployments. It summarizes the estimation accuracy depending on the pipematerial and size.

As shown in Table V, the mean estimation error is within 2.5%, regardless of thepipe material or pipe diameter. It is also interesting to note that the rigidity of thepipes does not affect the estimation accuracy, for example, the mean error for theplastic hose is 0.76%, and the mean errors for the two 1/8" threaded pipes are 1.02%and 2.12%, respectively. The mean estimation errors for the other solid pipes are alsosimilar.

6. EXPERIENCE WITH LONG-TERM DEPLOYMENTS

The evaluation section proves that vibration-based flow estimation is feasible in re-alistic settings that have various pipe materials, sizes, sensor placements, exter-nal vibrations from everyday activities, and complex pipe topologies. In addition to



Fig. 15. Tracking performance from a 3/4" stainless pipe

Table V. Water Flow Rate Estimation Summary Table for Pipe Types

Pipe Type 3/4" Copper 3/4" PVC 1/8" StainlessMean error(%) 1.03 2.10 1.18Pipe Type 1/8" Copper 1/8" Threaded 1/4" Fine-ThreadedMean error(%) 1.05 1.02 2.12Pipe Type 3/8" Brass 3/8" Stainless 1 1/4" PVCMean error(%) 3.22 0.17 3.32Pipe Type 3/4" Stainless 1 1/4" Stainless Plastic HoseMean error(%) 1.24 0.19 0.76

performance, we discuss the following questions from our deployment experiences.(1) How long does it take to calculate the calibration parameters? (2) Does the sensornode achieve the estimated battery life, and what are the battery-drain characteristicsfrom the deployment? (3) How severe is the vibration propagation between pipes? (4)how much do external vibration sources affect the system operation? (5) What do welearn from the estimated water consumption trends?

In this section, we discuss our experiences with the single-family house deployment.To provide better context, Table VI describes the node IDs and pipe information.

6.1. System Adaptability

As described in Section 3, the system adapts to varying environments and tunes thecalibration parameters as necessary. The initial parameter calibration also has this


8:22 Y. Kim et al.

Table VI. Long-term Deployment Setup

Node ID Pipe Node ID PipeID100 Bath1 Cold ID101 Bath1 HotID102 Bath1 Toilet ID104 Laundry RoomID105 Kitchen Cold ID106 Kitchen HotID107 Bath2 Cold ID108 Bath2 HotID109 Bath3 Cold ID110 Bath3 Hot

0 2 4 6 8 10 12−50

0

50

100

150

200

250

Parameter Adaptation over Time

Time [day]

Nor

mal

ized

Cal

ibra

tion

Par

amet

er C

hang

es Node100Node105Node107Node109

Fig. 16. The monitoring system gradually learns the calibration parameters. As it learns, the calibrationparameters settle.

property. Figure 16 shows that the normalized calibration parameter10 changes overtime in the single-family house deployment. As shown in Figure 16, the monitoringsystem gradually learns the environments and tunes the calibration parameters asthe different water usage permutations occur. The parameters of each node graduallyreach a steady state. The time required for adaptation varies from one day to sevendays, depending on the water usage patterns. More time is needed when the waterusage pattern of a pipe is monotonic because the system needs longer to collect avariety of water consumption patterns. Note that the one-day recalibration step inFigure 16 provides a clearer view of the parameter adaptation steps. In reality, thisrecalibration occurs more frequently until the parameters are settled.

Note that Node 109 has more dramatic changes in the parameter values becauseits initial parameter feed was more off than the others. In the iteration, it had lesscomplicated water usage patterns than others, making the optimization solver needmore iterations until it collects sufficient samples.

Although the normalized calibration parameters are shown in Figure 16, only suf-ficiently accurate calibration parameters are used to report the estimated flow rate.The triggering of recalibration can be set depending on the desired estimation accuracyrequirement. In this experiment, we choose to use, but not be limited to, 10% for thetriggering.

10The normalized calibration value is the estimation error in %.



Fig. 17. An example of overlapping events: The vibration sensors differentiate water consumption by eachfaucet. This figure illustrates an example in which the first water faucet was turned on followed by thesecond water faucet.

Fig. 18. Vibration propagation between pipes is minimal since pipes are far from each other in most cases.Even when a sprinkler is on (from 6AM to 7AM), the observed vibration on a pipe from the node ID 100does not experience any significant vibration. Note that a spike at 6:20AM is due to a bathroom sink wateractivity.

6.2. Vibration Propagation in Real Deployment

In an earlier study [Kim et al. 2008], we explored the pipe crosstalk phenomena in alaboratory setting in which the pipes were closely located. To better estimate the flowrates under these circumstances, our modeling accounted for vibration propagationbetween the pipes.

In this study, we further investigated whether the vibration propagation could besevere during significant water-consuming activities, such as sprinkling. We foundthat vibration propagation occurs among closely connected pipes, whereas it is notsignificant if the pipes are farther from each other. In both cases, we also found thatpropagation is generally not as significant in the house deployment as in the laboratorysetting. For example, Figure 17 shows an event in which two faucets are simultaneouslyon. As shown in Figure 17(b), one faucet is turned on first, followed by the other. Thereis no vibration propagation between these two pipes. As shown in Figure 18, even when


8:24 Y. Kim et al.

0 2 4 6 8 10 12 14 16 18 20 22−2

−1

0

1

2

3

4

5Ambient Noise Characteristics

Days

Tim

e of

Ext

erna

l Vib

ratio

n[%

]

Fig. 19. In practice, vibration sensors are not prone to external vibration sources. This figure shows thetime of vibration sensors capturing external vibration. For most of time, it is less than 1% of time.

a sprinkler—the fastest water flow of all the water events in the house—is on (from6 AM to 7 AM), node 100 does not experience vibrations.

There is propagation between pipes that are close. For example, cold- and hot-waterpipes under a sink are placed closely together and experience vibration propagation.As discussed in our earlier study [Kim et al. 2008], our compensation mechanismsfor closely located pipes were used to improve the estimation accuracy. The improvedaccuracy was about five to ten time more accurate (from 53% error to 9% error [Kimet al. 2008]).

In general, however, pipes have many mounting points with tight brackets. As thedistance between pipes increases, the number of mounting points increases. The vi-bration propagation can be seen as wave propagation through pipes, which makes thepropagation insignificant because both longer distance and mechanical bonds act asstrong attenuation factors.

6.3. Observed External Vibration Sources

External vibration has an insignificant impact on system performance. Because thevibration sensors are externally attached to pipes, it is possible that external vibrationfrom various household activities can be observed by the vibration sensors, resultingin added flow rate estimation noise. While the correction mechanism discussed in theprevious section boosts the estimation accuracy, external vibration can make the flowestimation less accurate. We believe that it is important to understand the effect ofexternal vibration sources.

To study this effect, we monitored the vibration sensor values under no water flow,computed a histogram of the vibration measurement, and computed the percentile ofthe vibration data that is above the noise floor. Figure 19 shows the time-of-vibrationsensors’ external vibration readings over three weeks. We can see that the time ofexternal vibration that interfered with the pipes is less than 1% for all of the cases.Therefore, the vibration sensors are less prone to external vibration sources in practicethan in theory.

6.4. Battery Drain Characteristics and Node Lifetime Assessment

To confirm the node lifetime calculation, we monitored the battery level changes bymonitoring the voltage drop from the sensor nodes. Figure 20 depicts the power drainfrom the deployed sensors. Figure 20(a) shows the battery level changes from a telosBplatform used to model the battery level. Figure 20(b) shows the battery level changes



Fig. 20. Actual battery level changes from a long-term deployment. (a) The battery level change from atelosB platform used to model the battery level (data courtesy of Rahul Balani). (b) The battery level changesover 35 days from the long-term deployment. The nodes consumed approximately 8% of battery for thedeployment.

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000Diurnal Water Use[Breakdown]

Time[days]

Wat

er C

onsu

mpt

ion[

L]

Sprinkler/PoolLaundryMachineOthers

(a)

0 5 10 15 20 250

50

100

150

200

250

300

350

Time[days]

Wat

er C

onsu

mpt

ion[

L]

Water Use by End−point

Bath1−CBath1−HBath1−TKitchenLaundryRoomBath2−CBath2−HBath3−CBath3−H

(b)

Fig. 21. Water consumption now simply can be divided by each endpoint. (a) Water consumption by asprinkler, a laundry machine, and others. (b) Break-down of the consumption by each pipe.

during 35 days of the long-term deployment. The nodes consumed at most 8% of thebattery life during the deployment. We can linearly extrapolate the node lifetime fromthis data, which results in approximately 435 days.11

It is interesting to note that the battery level changes more slowly than the antici-pated rate.12

6.5. Water Consumption Breakdown

We now discuss the pipe-level water consumptions from the single-family house. Fig-ure 21 depicts the water consumption breakdown. The most water-consuming activitiesin this home are those of the sprinkler and those related to the pool, which accountfor more than 92% of total consumption. The sprinkler activity has an interesting

11Note, however, that the node lifetime can vary due to its nonlinear characteristics.12The actual battery life could be less than predicted due to other factors, such as natural battery drainfrom temperature fluctuations. Nevertheless, this result indicates that it would be possible to achieve a nodelifetime of a few years with a research sensor network platform and that it would be possible to achievelonger battery life in a dedicated sensing platform.


8:26 Y. Kim et al.

implication for sewer costs as well. This household does not have a submeter for thesprinkler units. In many US regions, the domestic sewer bill is determined by waterconsumption, assuming that the water consumed goes directly into the sewer system.Water consumption for sprinklers can be excluded from the sewer bill only if they haveauthorized submeters installed by utility providers. Therefore, this household pays ahigher sewer bill.

Another interesting statistic is the ratio of hot-water use to cold-water use. In thishousehold, the cold- and hot-water consumption ratio is 1:0.23. With this ratio, we canroughly estimate the energy cost of heating water for the entire household and for eachbathroom.

7. CONCLUSION

In this article, we developed and evaluated a vibration-based water flow monitoringsystem in various settings. We studied various aspects of its performance, such asmodel appropriateness, sensing stability, sensing sensitivity, dynamic range, trackingperformance, system adaptability, and long-term sensing system performance changes.In addition, we discussed practical issues and our experiences by addressing the nodelifetime, installation time, and deployment complexity.

We covered most types of domestic plumbing system pipes in the evaluation. Ourevaluation data confirm that vibration-based water flow rate estimation is feasible andeffective. Overall, we report that the average pipe-level flow estimation error achievedis less than 5% (with an error standard deviation from 4 to 12%).

The performance evaluation confirms that the estimated water consumption informa-tion could provide high-quality information for facilitating educated decisions on watersavings. For example, the residents can view water consumption statistics at endpointlevels, such as summaries of the water consumption by room, hot or cold water and timeof day. With this detailed consumption data, the residents can even determine how toreplace less efficient water fixtures and understand return-on-investment periods.

While the system can be used to fully monitor fixture-level consumption, the systemalso has several additional applications in simpler deployment scenarios. For example,it could be used as a submetering and incremental deployment system for the vibrationsensors. If a user is only interested in the breakdown between cold- and hot-water use,the user can install two vibration sensors (on cold- and hot-water pipe branches fromthe main pipe). Room-by-room monitoring is also possible by monitoring branch pipesthat are connected to different rooms. The current system consists of vibration sensors,relay nodes, and a handheld main meter. The installation time was not more than twohours, and no plumbing alterations were required. These properties mean that thesystem can also be used to quickly audit the water consumption of residential spaces.

Infrastructure monitoring, including fine-grained resource monitoring, is one exam-ple of a sensor network application in which the sensing nodes can leverage the existinginfrastructure. By making the sensing nodes as simple as possible and moving the net-working burdens to the infrastructure nodes, we achieved a longer node lifetime andthus a longer system lifetime (about 435 days with a one-second sampling interval).

8. FUTURE WORK

In this study, we chose to use a sampling time of 0.25 s and a 196-Hz sampling rate.While these settings provide fairly accurate flow estimation and extended node life-time, the optimal sampling rate and interval needs to be further investigated. In addi-tion, adaptive and predictive sampling approaches for reducing wasteful sampling andprocessing are of future interest.

Although we demonstrated the feasibility of our proposed system using a long-termstudy, the current solution is not free of limitations. First, the ultrasonic flow meter



that was used in this particular experiment is a highly accurate measurement unit. Acheaper way of instrumenting the main water meter is necessary for wider adaptationsof this technology. Fortunately, a water meter capable of automatic meter readingis currently being deployed [American Water Works Association 2005; Chen et al.2011]. However, its temporal granularity is typically coarse. Further research on theimplications of coarse temporal granularity is of interest.

Our system exploits the small vibrations from steady-state water flow. When thewater is forced to stop or change direction, the water hammering effect creates anextra pressure surge and vibrations in domestic plumbing systems [Bruce et al. 2000].Because it is only transient in low-rise buildings, our experiment was not adverselyaffected by this limitation. However, high-rise buildings that use water pumps experi-ence a continuous water hammering effect. To address this limitation, future researchis needed to extend the model, validate the extended model, and test it.

ACKNOWLEDGMENTS

The authors would like to thank to Thomas Schmid, Jonathan Friedman, and Anna Davitian for their helpsin the prototype system design.

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Received June 2011; revised October 2011; accepted October 2011


a longitudinal study of vibration-based water flow sensing

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