Electric water heaters are responsible for a large portion of electricity consumption and water usage in the domestic sector. Smart water heaters alleviate the strain on the electricity supply grid and reduce water consumption through behavioural change, but the installation of in-line ow meters is inconvenient and expensive. A non-invasive water ow meter is proposed as an alternative . Non-invasive ow measurement is more common for high ow rates in the industrial sector than for domestic applications. Various non-invasive water measurement methods are investigated in the context of domestic hot water, and a combination of thermal- and vibration-sensing is proposed. The proposed solution uses inexpensive, easily installable, non- invasive sensors and a novel algorithm to provide the same ow measurement accuracy as existing in-line meters. The algorithm detects the beginning and end of water consumption events with an accuracy of 95:6 %. Quantitative ow rate estimation was possible for ow rates greater than 5 L min1with an accuracy of 89 %, while volumetric usage estimation had an accuracy of more than 93 %. The algorithm limitations were applied to eld data, revealing that water consumption could be detected with an error of less than 12 % within the limitations of the proposed algorithm. The paper presents a successful proof of concept for a non-invasive alternative to domestic hot water ow rate measurement. Keywords: Hot water ow estimation, smart water heaters, smart grid. 1. Introduction Water heating with EWHs contributes to 34 % of residential electric energy consumption, which can be reduced with the use of smart EWH controllers (SECs) (de la Rue du Can et al., 2013). Based on known hot water demand patterns, individualised heating schedules and temperature set points can be used by SECs to reduce energy consumption due to water heating without a ecting user comfort (Kepplinger et al., 2016; Booysen and Cloete, 2016; Jack et al., 2018; Armstrong et al., 2014). Widespread use of SECs can decrease the strain on the electricity supply grid through peak shaving by implementing demand-side management, which schedules when EWH heating elements can be active, while taking consumer comfort and hot water demand into account (Jack et al., 2018; Roux et al., 2017, 2018). SECs can also decrease the total domestic water consumption by providing users with detailed water consumption feedback. Studies have shown that users who receive consumption feedback decrease their water consumption by adjusting their water usage behaviour (Liu et al., 2017; Ripunda and Booysen, 2018; Fielding et al., 2012b,a). A limiting aspect of the large-scale deployment of SECs is the non-trivial and expensive plumbing required to install an in-line water ow meter to measure hot water consumption. A non-invasive, retro t domestic hot water measurement system removes the expensive plumbing associated with SEC installation. This paper addresses this problem by proposing a novel non-invasive ow sensor that uses vibration and temperature sensing to estimate hot water ow through copper piping. Several non-invasive technologies were investigated in the context of domestic EWH conditions. A combi- nation of vibration and outlet pipe temperature analysis was determined to be the most practical solution. A non-invasive water ow meter for a smart EWH controller was developed using a novel algorithm that requires Corresponding author Email address: mjbooysen@sun.ac.za (M.J. Booysen) Preprint submitted to Elsevier July 21, 2018Preprint of paper accepted for publication : https://doi.org/10.1016/j.flowmeasinst.2018.07.003 Table 1: Summary of non-invasive water ow rate studies Evans et al. (2004)Bernier and Bren- nen (1983)Huijsing et al. (1988)Safari and Tavas- soli (2011)Jacobs et al. (2015)Nel et al. (2015)This paper Domestic ow rates 7 7 7 3 3 3 3 Water as working uid 3 3 7 3 3 3 3 Low-cost sensing 3 7 3 3 3 3 3 Copper pipe supported 3 7 3 3 7 3 3 Robust (noise and location) 3 7 3 7 7 7 3 temperature and accelerometer data only. The non-invasive ow estimation algorithm was developed using an experimental EWH unit, which was designed to re ect domestic conditions. The selected temperature sensors and accelerometer are inexpensive and readily installed in existing systems, providing an economical retro t solution. 2. Related Work Table 1 lists relevant investigations into non-invasive water ow sensors. Non-invasive uid measurement is common in industrial conditions (Pereira, 2009). Larger pipe diameters and higher uid ow rates are typically present in industrial conditions than can be expected for domestic EWH conditions. D ata from 34 domestic SEC eld units showed maximum measured volumetric ow rates of 30 L min1(Roux et al., 2017). In contrast, industrial applications discussed by Evans et al. (2004) exhibit ow rates between 500 L min1 and 1500 L min1for similar pipe diameters. Lower domestic water ow rates often mean that industrial non-invasive ow measurement methods are not suited. Ultrasonic and electromagnetic methods are commonly employed for the non-invasive measurement of uid ow. The use of ultrasonic transducers is technically feasible for domestic use (Sanderson and Yeung, 2002), but too expensive for the desired application as components costs alone would exceed current in-line installation method costs. Electromagnetic ow measurement requires an electrically non-conductive inner pipe lining , precluding their use with copper piping (Bernier and Brennen, 1983; Shercli , 1987). Thermal methods are generally used to measure gas ow rate (Pereira, 2009). Thermal mass (or thermal dispersion) ow measurement was used by Huijsing et al. (1988) to measure low ow rate liquid ows (below 0:6 L min1) in small diameter pipes (the measuring tube has an inner diameter of 13 mm). Thermal event detection and volumetric estimation were incorporated in an EWH energy usage model by Nel et al. (2015) using a non-invasive temperature sensor installed on the outlet pipe. The data sample rate used was 1 min and the described system was more e ective for longer duration ow events (7 to 10 min) and the minimum duration of a detectable usage event was 3 min. Domestic water ow conditions are almost exclusively turbulent. Rapid velocity uctuations generated by turbulent ow results in vibrations on the pipe surface, and the magnitude of these vibrations are correlated to the average uid velocity in the pipe (Evans et al., 2004). An empirically derived quadratic relationship was found between the standard deviation of the vibrations measured using an accelerometer and uid velocities ranging between 1 :82 m s1and 5:48 m s1(Evans et al., 2004). These velocities are common in industrial conditions, but greater than that found in domestic applications where the maximum uid velocity is approximately 0 :64 m s1. Another study utilizing condenser microphones to detect vibrations found either linear or quadratic correlations, depending on the sensor position (Safari and Tavassoli, 2011). Time and frequency domain analysis were used to estimate water ow using a piezoelectric transducer installed on a tap outlet, but transitional water ow rates could not be estimated accurately (Jacobs et al., 2015). From the above information, a combination of vibration and thermal water ow estimation was identi ed as being the most promising method for low-cost non-invasive ow measurement and were further investigated in the context of domestic EWH conditions. 2 3. Experimental Unit 3.1. Hardware A 150 L EWH with a 3 kW heating element and a 600 kPa water supply, as is commonly found in domestic installations, was selected. A diagram of the experimental unit is shown in Fig. 1. A Raspberry Pi 3 was used to sample the sensors, store acquired data, and perform scheduled water usage events for controlled experimental conditions. Water ow rate was controlled using a manually operated ball valve and scheduled water usage ( ow events) were controlled by fully opening or closing an electrically operated solenoid valve. Water ow rate was measured using an in-line positive displacement Misol ow meter with a volumetric measurement resolution of 380 pulses per litre and general purpose input/output (GPIO) interrupt handler in software. Two temperature sensors were mounted on the EWH outlet pipe: one `near' ( TN) and one `far' ( TF) a short distance away from the EWH outlet. Inlet pipe ( TIn) and ambient air ( T1) sensors were also installed, but were not required for the designed system to function. Texas Instruments TMP275 digital temperature sensors were selected due to their relatively low cost, listed accuracy of 1C without calibration, inter-integrated circuit (I2C) communication, and maximum resolution of 12-bit which equates to 0 :0625C. Heatsinks were installed on the outlet pipe to maximize the longitudinal temperature di erence on the outlet pipe between the upstream and downstream sensors. The heatsinks were milled to have a 22 mm mounting surface to enclose the outlet pipe. This was to provide a `best case' scenario for thermal investigations. The study indicated that sucient thermal data was available for the experimental unit that heatsinks and `far' temperature sensors were not required - but this cannot be con rmed for other installations until eld tests are performed. An LSM303 3-axis accelerometer was installed on the inlet pipe, suciently far from upstream and downstream disturbances to ensure fully developed turbulent ow was measured. 3.2. Software A python script was executed on the Raspberry Pi to control the water ow for experiments using the solenoid valve, sample the temperature sensors and accelerometer using I2C, measure the water ow rate using GPIO pulses, and to store the acquired data in a MySQL database. Data sampling was performed at 1 s intervals. Accelerometer sweeps were performed at 1 kHz and the standard deviation of 250 g- force readings per accelerometer axis were stored. The values were ltered using a centre-shifted rolling mean (moving average) lter with a window length of 10 s to smooth the signals while maintaining temporal accuracy. Experiments with automated ow events were controlled using the Raspberry Pi and solenoid valve to ensure repeatable conditions. 3.3. Experimental plan Three separate experiments were performed using the EWH unit to test di erent aspects of the system. The associated datasets were used to design and test the non-invasive ow estimation algorithm. Table 2 summarises the purposes of each dataset. Dataset 1 consisted of 5 days of scheduled ow events at a xed ow rate for each test day. Four clusters or sets of three ow events were executed 6 h apart during each test day. The three ow events which formed EWHRPi FMHS TInTN TF Acc.SVBV T∞ Cold inletHot outlet Figure 1: Diagram showing the experimental unit. Outlet pipe temperature sensors (near and far - TNandTFrespectively), inlet pipe temperature sensor ( TIn), ambient air temperature sensor ( T1), heatsinks (HS), electrically operated solenoid valve (SV), manually operated ball valve (BV), ow meter (FM), EWH tank, LSM303 accelerometer and Raspberry Pi (RPi) are shown. 3 Table 2: Experimental Unit Dataset Summary Dataset Purpose Flow Control 1: Scheduled Flow EventsDesign Flow Estimation Algorithm Scheduled Repeat Testing Minimum Vibration Sampling Requirements 2: Manual Flow EventsTest Instantaneous Flow RatesManual Test Short Duration Events 3: Scheduled Cool Down Time Determine Min Cool Down Time Between Events Scheduled each of the daily \test sets" were: a 2 min ow event (followed by 3 min of no ow), another 2 min ow event (followed by 3 min of no ow), and a 5 min ow event. Repeated ow events at xed ow rates for each day of testing provided sucient data to design the ow estimation algorithm. Dataset 2 consisted of manually controlled ow events executed with the intention to test instantaneous ow rate estimation and the e ectiveness of the algorithm for shorter ow events. Dataset 3 consisted of scheduled 1 min ow events with increasing time of no ow between ow events. This was done to determine the minimum cool-down time required between ow events for the algorithm to accurately identify ow events. 4. Flow Estimation Algorithm The algorithm combines event detection, which provides temporal boundaries of non-invasively detected water ow events, and ow estimation, which provides quantitative volumetric ow estimation values for eligible detected usage events. 4.1. Event Detection The non-invasive detection of hot water consumption (valid usage events) consisted of two distinct steps. Vibration data was used to ag time-points where the measured vibration standard deviation exceeded empirically determined thresholds,  > (min). Consecutive agged samples were grouped together to form "vibration events" which contain the temporal boundaries (start and stop times) of potential usage events. Some detected vibration events were found to contain no measured water consumption. Thermal event classi cation used temperature data during agged vibration events to determine whether water ow or external vibration interference was responsible for each grouped vibration event. Four thermal criteria, TC, were developed. The near temperature (upstream of heatsinks), TN, and far (downstream of heatsinks), TF, were used to determine the thermal criteria as shown: TC1:TNmust be above 40C at the end of an event. TC2:TFmust be above 35C at the end of an event. TC3: Longitudinal temperature di erence ( T=TNTF) must be below 8C at any time during an event. TC4: Time di erential of near sensor ( _TN) must have a peak value greater than 0 :15C=s within 15 s of the start of an event. If all four thermal criteria were met during a vibration event, then the vibration event was classi ed as a usage event. Vibration events which did not ful ll all the thermal criteria were classi ed as interference events. 4 4.2. Flow Estimation Once it was determined that a agged event corresponded to actual hot water consumption, ow rate estimation was performed using the vibration data. An adaptation of the relationship described by Evans et al. (2004) was used to relate vibration standard deviation, , to volumetric ow rate, _V(rather than to uid velocity as by Evans et al. (2004)). A basic linear approximation between and the measured volumetric ow rate, _VM, was found to provide better results than a basic quadratic approximation for the experimental unit. The dataset is available in the supplementary data in Appendix A. Accurate tracking of instantaneous ow rates during certain ow events was observed for ow rates > 5 L min1. Accurate average estimated ow rates for an event with instantaneous ow rate uctuations indicate that the linear approximation used was sucient for medium and high ow rates. Low ow rate events ( 5 L min1) were consistently detected with usage event detection as ow events, but quantitative ow rate estimation was found to be unreliable. In the usage event detection phase, it was found that grouped vibration data could be used to determine whether each respective usage event contained ow rates which could reliably be quantitatively estimated. A second set of threshold values was established corresponding to the minimum measured values for usage events which contained acceptable ow estimation accuracy. Low ow events were thus marked as \unreliable" meaning that quantitative ow estimation would not provide accurate results. Qualitative estimation was investigated for unreliable usage events. Higher ow rate events contribute more to volumetric consumption in the same time span, so estimation errors at low ow rates are likely negligible. Vibration data sampled Not flow Group consecutive samples marked as vibration event Four thermal criteria met? Vibration marked as hot water usage 𝝈>𝜎𝑅𝑇ℎ? 𝜎𝑥,𝑦,𝑧>𝜎𝐸𝑇ℎ? Volume of usage event from integral of flow rateAssume constant low flow rateFlow rate estimate based on vibration data Figure 2: Non-invasive ow rate estimation diagram representing logic used to detect potential ow events using vibration analysis, detection of usage events using thermal analysis, and quantitative ow estimation for events which will yield reliable results based on vibration analysis. ETh is the threshold for considering vibration as a potential event. RTh is the threshold above which ow rate can be reliably estimated. 5 0 2 4 6 8 10 12 14 16 18 2005101520 Ev en t Duration Ov erestimation [ % ]OccurrenceSc heduled Flo w Ev en ts Man ual Flo w Ev en ts Sc heduled Co ol-do wn TimeFigure 3: Temporal over-estimation of vibration event detection. 5. Experimental Results 5.1. Limitations Two algorithm limitations were observed during the design process. The rst limitation relates to event detection. Thermal event classi cation was not successful when insucient cooldown time, tcd<2 min, between ow events was observed. The temperature of the outlet pipe must decrease slightly between ow events for the thermal criteria to be met, otherwise usage events were incorrectly classi ed as interference events. The second limitation is that quantitative ow rate estimation was only possible for ow rates greater than a minimum value of_V(min)5 L min1. 5.2. Event Detection 5.2.1. Temporal Boundaries The non-invasive detection of temporal boundaries of ow events was performed using vibration data. The temporal accuracy of the detected boundaries was assessed by comparing the duration of measured water ow during a vibration event to the non-invasively determined duration of an estimated usage event. It was observed that vibration event detection over-estimated the duration of usage events. It is likely that vibration propagation from the solenoid valve and ball valve contributed to the observed temporal over-estimation. The two ow control valves were situated much closer to the EWH cylinder than the nearest downstream ow control valve in domestic installations. Fig. 3 shows a histogram of the non-invasive temporal over-estimation of an event as a percentage of the measured duration (using ow meter data). Temporal boundaries were accurate for Scheduled Flow Events, which consisted of ows 2 min and 5 min in duration. Temporal boundaries were less accurate for Manual Flow Events of short duration. Scheduled Cool-down Time events consisted of 1 min duration ow events and consistent temporal over-estimation can be seen for these events (corresponding to the 7 s of solenoid toggle time per event, which is 11 % of the scheduled duration of the ow events). 5.2.2. Usage Event Detection Thermal event classi cation was performed for grouped vibration events to non-invasively determine which vibration events were due to hot water ow and which must be disregarded. Table 3 shows the summary of usage event detection in datasets 1 to 3 (Scheduled Flow Events, Manual Flow Events and Scheduled Cool-down Time respectively). The success of using vibration data to identify reliable usage events which can receive quantitative ow rate estimation is also shown. Fig. 4 shows the measured temperatures of 3 scheduled usage events and TC1,TC2andTC3. The solid line sections of the measured temperatures show where vibration events occurred, and the dotted sections show where no vibration event was detected. The solid sections thus show the non-invasively determined temporal boundaries of each vibration event wherein thermal event classi cation takes place. Fig. 5 shows the fourth thermal criterion used which is that a suciently large temperature gradient must be measured for the upstream temperature within 15 s of the start of a vibration event. It was observed thatTC4was not met when there was insucient cool-down time between successive water ows. TC4was 6 -5 0 5 10 15 20010203040 Time [ min ]T emp erature [◦C ] TN TF ∆T TN(min ) TF(min ) ∆T(max )Figure 4: Thermal Criteria 1, 2 and 3 for Event Classi cation. TC1:TN40C (blue),TC2:TF35C (green),TC3: T 8C (red). -5 0 5 10 15 2000.20.40.60.81 Time [ min ]T emp erature Gradien t [◦C s−1] ˙TN ˙TN(min ) Figure 5: Thermal Criterion 4 Relating to Time Derivative of the Upstream Temperature Sensor. TC4:_TN0:15C s1 within 15 s of event start (red). Table 3: Experimental unit event detection summary. DatasetUsage Events Reliable Events Expected Detected Expected Detected 1 60 55 45 45 2 12 0 8 8 3 13 6 13 13 however necessary to remove the chance of incorrect classi cation of external vibration events occurring after valid water ow while the outlet pipe is still warm (which would meet TC1;2;3). Strict thermal criteria (which includesTC4) were used to avoid large consumption overestimations due to vibration interference events. Table 3 shows that 55 of the 60 scheduled hot water ows were correctly classi ed as usage events with the remainder occurring during times of external vibration interference. No false positives were found in any dataset but false negatives were observed during external vibration interference in dataset 1 . The algorithm limitation of a minimum cooldown time, tcd, between events was observed during analysis of dataset 2 (consisting of manually controlled ow events). All ow events in dataset 2 were classi ed as interference events. Further experiments were performed to determine tcd, using dataset 3 (Scheduled Cool- down Time). Manual classi cation of vibration events in da tasets 2 and 3 was done to enable more detailed analysis. The combined e ect of the temporal boundary accuracy and the classi cation of events was assessed by determining what temporal percentage of all measured ow events were valid in dataset 1. Table 4 shows the percentage of duration of all vibration events which were detected during scheduled ow events. Interference 7 Table 4: Dataset 1 usage event detection summary. Event Classi cation Valid [%] Invalid [%] Usage 86.7 3.6 Interference 8.7 1.0 Total 95.4 4.6 0 5 10 15 20 25 3001020304050 Time [ min ]Flo w Rate [ L min−1]˙VM˙VE ¯˙VM¯˙VE Figure 6: Flow Rate Estimation. events occurring during ow tests are included. It can be seen that events were correctly classi ed 95 :4 % of the time which shows that usage event detection using non-invasive vibration and temperature data was successful using the algorithm. 5.2.3. Reliable Event Detection The algorithm is only able to provide reliable quantitative ow rate estimation above_V(min)of 5 L min1. It was found that the average vibration standard deviation,  , for grouped events could non-invasively identify events with measured ow rates greater than 5 L min1. These events were agged as being `reliable' and thus eligible for quantitative ow estimation. Table 3 shows that the identi cation of reliable usage events was completely successful because all expected reliable usage events were detected. This means that the duration of low ow rate water consumption is known and that a xed low ow rate approximation can be used for these events. Quantitative ow estimation was performed for reliable usage events. 5.3. Flow Estimation 5.3.1. Instantaneous Flow Rate Estimation Fig. 6 shows that the estimated ow rate, _VE, and measured ow rate, _VM, are similar for instantaneous ow rate changes in dataset 2. The ow events were manually controlled to test a larger variety of ow rates. Large spikes in _VEcan be seen at the start and ends of usage events, indicating that the manually operated ball valve generated larger vibrations which caused the ow rate overestimation at times. Instantaneous ow estimation can be seen to be accurate for the usage event starting 20 min into the manually controlled ow events experiment. This event had a long duration (so the vibrations associated with the ball valve did not in uence the temporal boundaries as severely as for short events), but contained instantaneous ow rate changes. This indicates that the linear relationship used to estimate ow rates is valid because the algorithm was successful for a wide range of ow rates in a single usage event. 5.3.2. Average Flow Rate Estimation The average estimated and measured ow rates,_VEand_VM, are shown in Fig. 6 as dashed lines with end markers. It can be seen that the estimated ow rate is accurate for certain usage events. Usage events with longer durations were more accurately estimated than short events. Dataset 2 also had the greatest 8 0 2 4 6 8 10 12 14 16 18 20 22100101102103 ¯˙VM [L min−1]Absolute¯˙VE Error [%]Sc heduled Flo w Ev en ts Man ual Flo w Ev en ts Sc heduled Co ol-do wn TimeFigure 7: Flow Rate Estimation Error and Flow Rate Scatter Plot. temporal boundary errors (as shown in Fig. 3) so the manual operation of the ball valve on the outlet pipe was suspected to contribute to the inaccuracy observed. 5.3.3. Estimation Error Fig. 7 shows the absolute ow rate estimation for all 80 detected usage events in datasets 1 to 3. The vertical line at 5 L min1shows_V(min)which is the ow rate value to separate qualitative and quantitative ow rate estimation. Low ow rates have an estimation error which is an order of magnitude greater than higher ow rates, which demonstrates the need to determine which detected usage events could be reliably estimated. Higher ow rates have a reasonably consistent estimation accuracy for the ow rates acquired using the experimental EWH unit. Quantitative ow rate estimation was thus only performed for usage events which were classi ed as reliable events using vibration data. Fig. 7 shows quantitative ow rate estimation errors for reliable scheduled usage events were below the desired margin of 10 % (with the exception of one Scheduled Flow Event which had an estimation error of 11 %). Estimation errors were greater for manually controlled ow events due to the temporal overestimation associated with vibrations caused by the ball valve. 5.3.4. Volumetric Consumption Estimation It has been shown that non-invasively determined temporal boundaries of hot water consumption events are accurate, ow rates greater than 5 L min1can be estimated within the desired accuracy for expected real- world conditions, and usage events can be non-invasively classi ed to determine if quantitative ow estimation is possible. Fig. 8 shows a histogram of the error between estimated and measured volumetric consumption values for each reliable usage event. The volumetric errors are generally low, especially for datasets 1 and 3 which use the automated solenoid valve to control ow. Table 5 shows the average measured ow rate, total measured consumption, total estimated consumption, and consumption error for the 5 days of scheduled ow events in dataset 1 (external vibration interference are excluded). It can be seen that experimental run 1, with_VMof 1:63 L min1, had an unacceptably large estimation error of 195 :72 %. All events occurring during experimental run 1 were marked as unreliable by the algorithm. Experimental runs 2 to 5 had mean volumetric estimation errors which are below the desired estimation accuracy of 10 %. In the above analyses, th measured ow rate, _VM, and vibrations during detected usage events were ana- lyzed to determine the relationship between ow rate and vibration standard deviation for the experimental unit. A universal relationship cannot be expected for all EWH installations. The piping geometry of each installation a ects the vibration propagation so calibration will be required during installation. The desired simplicity of installation and calibration was considered when designing the quantitative ow rate estimation aspect of the algorithm. An example of on- site calibration would be to connect an in-line ow meter to the outlet of a tap and record the ow measurement data for controlled ow events performed by an installation technician. This data can be used to calibrate the non-invasive algorithm for further use. 9 −5−4−3−2−1 0 1 2 3 4 5 60246 ¯VE Error [ L ]OccurrenceSc heduled Flo w Ev en ts Man ual Flo w Ev en ts Sc heduled Co ol-do wn TimeFigure 8: Volumetric Estimation Error for Reliable Usage Events. Table 5: Dataset 1 volumetric consumption estimation. Experimental_VMPVMPVE % Error Run [L min1] [L] [L] [%] 1 1.63 47.69 141.02 195.72 2 12.23 446.09 465.82 4.42 3 8.40 306.22 287.03 -6.26 4 10.08 369.19 362.62 -1.78 5 12.13 332.86 338.97 1.83 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34020406080100 Field Unit IDP ercen t of T otal Consumption % ] VE(Reliable )VE(Approx )VM(Ideal ) Figure 9: Low Flow Rate Approximation in Field Users Compared to Ideal Measurable Volume. 5.4. Performance of the method on eld data The algorithm is subject to limitations of a minimum cool-down time between ow events ( tcd2 min) and a minimum ow rate (_V(min)5 L min1) to perform correctly. A eld dataset containing the measured water consumption over a period of 4 weeks of 34 anonymous SECs users was acquired. The eld dataset was analysed to determine the severity of tcdand_V(min)limitations for real- world usage. This enabled the performance of the designed algorithm to be simulated for real- world conditions. Fig. 9 shows the percentage of the monthly water consumption which can be estimated using di erent methods for each user in the eld dataset by applying the algorithm limitations to the measured user con- sumption patterns. The volumetric contribution of events which are more than 2 min apart and contain ow rates greater than 5 L min1are shown in blue by _VE(Reliable ). This represents the percentage of each user's consumption which can be reliably estimated when both algorithm limitations are implemented. The estima- tion value when a constant low- ow approximation is implemented is shown stacked in orange by _VE(Approx ). An approximate low ow value of 2 L min1was used (based on the measured ow rate for events less than 10 20 40 60 80 10002468 Estimation A ccuracy [ % ]OccurrenceVE(Reliable ) 20 40 60 80 100 Estimation A ccuracy [ % ]VE(Approx )Figure 10: Low Flow Approximation In Field Units to Improve Performance. Table 6: Low ow approximation and portion of measured consumption which would be estimated. MethodPercentage of Total Measured consumption [%] Mean Std Min Q1 Q2 Q3 Max VE(Reliable ) 60.6 21.9 8.5 46.9 64.4 75.4 93.7 VE(Approx ) 89.0 6.7 68.5 86.7 90.9 93.6 99.4 _V(min)for the 34 anonymous SEC users). A reference value of the ideal measurable volume, _VM(Ideal ), is shown stacked in green. _VM(Ideal )is the percentage of volumetric consumption when only tcdlimitation is implemented on the dataset (the measured volume during detectable events). The reliably estimable volumetric consumption for users (blue _VE(Reliable )bars in Fig. 9) range between 8 % for poorly performing users to 93 % for the best performing user. This is due to user consumption patterns di ering. Certain users are therefore very likely to bene t from using the basic non-invasive system while others will not bene t. Without consumption information, it is not possible to determine whether a user is likely to be a good candidate. _VE(Approx )can be seen to improve user consumption estimations to close to the ideal estimation value, _VM(Ideal ), and improve the performance for all users. Fig. 10 shows the performance increase when using low- ow approximation for the eld dataset. The estimation accuracy, as a percent of the total measured consumption for each user, increases dramatically for poor performing users and additionally bene ts better performing users slightly. Table 6 shows the mean, standard deviation, minimum, rst quartile, median, third quartile and maximum consumption estimation values. Poorly performing users receive the greatest bene t from low- ow approximation as the minimum value increases from 8 :46 % to 68:45 %, and the rst quartile increases from 48 :89 % to 86:74 %. Low- ow ap- proximation also provides more consistent consumption estimation values for di erent users (as the standard deviation decreased from 21 :92 % to 6:96 %). 6. Conclusion This paper evaluated the potential of performing non-invasive ow rate estimation for domestic EWH conditions using temperature sensors and an accelerometer. The designed ow estimation algorithm utilised the combination of vibration and temperature data to non-invasively detect hot water usage events and estimate consumption ow rates and volumes. The algorithm was designed and tested using an experimental EWH unit. The ow estimation algorithm was limited to a minimum time of 2 min between hot water consumption events for e ective usage event detection, as well as a minimum ow rate of 5 L min1for quantitative non- invasive ow estimation. These limitations were applied to a eld dataset containing real world consumption data and the performance was acceptable when low- ow approximation was implemented. The relatively inexpensive sensors did not require a complex installation procedure which was the intention (to encourage potential users to install a SECs unit). The proposed solution was proven, but further testing and development is required to determine if the algorithm can be universally successful. Under these conditions, the designed ow estimation algorithm provides an a ordable alternative to the existing invasive ow measurement method for the non-invasive 11 measurement of hot water demand, which can be used to reduce the energy used to heat water in a smart grid with schedule- and temperature-controlling SECs. 7. Acknowledgement The authors would like to thank MTN for their nancial and technical support through the MTN Mobile Intelligence Lab. happy hour