The ow estimation algorithm was observed to have 2 limitations which inhibited universal operating conditions. The rst limitation was that a minimum cool down time,xtcd, between usage events must be present. This is so that the pipe and water can su ciently cool down so that usage event detection can be successfully performed using the thermal
criteria. The second limitation was that quantitative ow rate estimation was not possible for ow rates below ¯˙V(min) 5 L min−1. Events which cannot be quantitatively estimated were correctly identi ed in 100 % of cases observed in Datasets 1, 2 and 3 as demonstrated in Section 6.2.4.
tcd : 2 min Cool down time between ow events for thermal event classi cation to be possible
¯˙V(min) : 5 L min−1 Minimum ow rate for reliable quantitative ow rate estimation
6.3.1 Cool Down Time Limitation
The thermal criteria explained, in Section 5.2.2, were used to classify vibration events as usage events or interference events using thermal data. The thermal inertia of the copper pipe and enclosed water meant that the pipe cooled down at a certain rate. Temperature gradients had to be used as one of the thermal criteria to eliminate interference events which could occur shortly after the end of a valid usage event. If su cient time was not given between usage events for the system to cool down then the thermal criteria were not met and ow events were classi ed as interference events.
Insu cient cool down time, tcd, between events caused all ow events in Dataset 2 to be incorrectly classi ed as interference events as shown in Table 6.1.
Further experiments were conducted to establish tcd as discussed in Section 4.5.3 to ge- nerate Dataset 3. Dataset 3 showed that a minimum cool down time, tcd, of 2 min was required for usage event detection to perform as expected (meaning that the thermal criteria were met).
In Section 6.6 the cool down time limitation is applied to the Field Dataset to establish what number of measured usage events would not have been detected because of this limitation.
6.3.2 Flow Rate Limitation
Quantitative ow rate estimation was observed to be relatively consistent for certain ow events. Low ow rates were observed to have an order of magnitude larger error than the rest of the usage events. It was possible to identify usage events which contained low ow rate measurements using vibration analysis as shown in Section 6.2.4. Qualitative estimation was thus possible for low ow rates, and quantitative estimation was possible for ow rates greater than a minimum threshold.
The minimum ow rate threshold, ¯˙V(min), was observed to be 5 L min−1. This value was determined by isolating ow events which had the largest estimation error and investiga- ting trends. Measured ow rates which fell below the minimum threshold had inaccurate estimations, and the corresponding σ values all fell below certain vibration thresholds which were consistently identi ed as shown in Table 6.1.
Only reliable ow rates were quantitatively estimated for the experimental unit; low ow regions were marked as unreliable meaning that qualitative estimation would not yield accurate results. The application of a xed approximated value was investigated to give at least some indication of the contribution of low ow rates to total volumetric consumption.
CHAPTER 6. RESULTS 88 In Section 6.6 the ¯˙V(min) limitation for quantitative ow rate estimation was applied to the Field Dataset. This showed the contribution that low ow rates (which can receive qualitative estimation only) had to the total monthly water consumption in real world applications.
6.4 Flow Rate Estimation
Flow rate estimation was performed for detected usage events. Quantitative ow rate estimation was found to be possible above ¯˙V(min) of 5 L min−1. Instantaneous ow rate estimation, ˙VE, was rst performed and con rmed to be accurate which to show that the linear proportionality between uid velocity and accelerometer standard deviation, σ, was correct. Mean ow rate estimation, ¯˙VE, was then performed and con rmed to be accurate which indicates that the temporal boundaries and instantaneous ow rate estimation were accurate.
6.4.1 Instantaneous Flow Rate Estimation
The rst stage of ow rate estimation is calculating an instantaneous ow rate estimate using the σ values for each sample in conjunction with their respective calculated constants as explained in Section 5.3. The instantaneous estimated ow rate, ˙VE, accurately tracks the measured ow rate, ˙VM, when the ow rate is adjusted during an event. There was only one example of such a scenario in the Dataset 1 during Test Set 3.1.
14:55 15:00 15:05 15:10 15:15 15:20 0 10 20 30 Time Flo w Rate [L min − 1 ]
Instantaneous and Mean Flow Rate (Set ID: 3.1) ˙
VM V˙E
¯˙
VM V¯˙E
Figure 6.5: Instantaneous and mean ow rate estimation. The instantaneous me- asured and estimated ow rates, ˙VM and ˙VE, are shown as solid lines and can be
seen to uctuate. The mean measured and estimated ow rates, ¯˙VM and ¯˙VE, for
each usage event are shown using dashed lines and end markers. The opaque line sections indicate regions where usage events were detected and the semi-transparent sections were not detected as events.
Figure 6.5 shows the measured and estimated instantaneous ow rates gathered during Test Set 3.1 in Dataset 1. The ow rate was adjusted while the automated solenoid valve
was open during the shown experiment. The ow rate was decreased during a scheduled ow event because the ow rate was observed to be too high. The 15:00:00 to 15:02:00 scheduled event is the only event in Dataset 1 where the ow rate was adjusted while water was owing. It can be seen from Figure 6.5 that the estimated ow rate corresponds well with the measured ow rate for a changing instantaneous ow rate.
Additional experiments were performed to generate Dataset 2 where varying ow rates were intentionally executed. The manually controlled ow events in Dataset 2 occurred with insu cient cool down time between events, so thermal event classi cation was not possible for ow events in Dataset 2. Detected vibration events were manually con rmed to be usage events using the ow meter data (which would not be available for a non- invasive system) 16:00 16:05 16:10 16:15 16:20 16:25 16:30 0 10 20 30 40 50 Time Flo w Rate [L min − 1 ]
Flow Rate Estimation for Dataset 2 ˙
VM V˙E
¯˙
VM V¯˙E
Figure 6.6: Dataset 2 ow rate estimation. The instantaneous measured and esti- mated ow rates are shown as solid lines, ˙VM (blue) and ˙VE (red) respectively. The
mean measured and estimated ow rates for each usage event are shown as dashed lines with end markers, ¯˙VM and ¯˙VE respectively. The regions where vibration events
were detected are shown as opaque lines and regions where not vibration events were detected are shown as semi transparent lines.
Figure 6.6 shows the instantaneous and mean ow rates for Dataset 2. The data in Dataset 2 did not contribute to the calculation of the ow rate estimation constants used in the system. The information from Dataset 2 can thus be viewed as the rst new ow information after calibration was completed (or after the algorithm was designed using Dataset 1).
It is apparent from Figure 6.6 that measured ow rates less than 5 L min−1 cannot be accurately estimated. It can also be seen from the ow occurring between 16:20 and 16:23 that instantaneous ow rate estimation is possible for an extended duration event. It can be seen from gures 6.5 and 6.6 that ˙VM and ˙VE correspond closely for ow rates greater than 5 L min−1 even for uctuating usage during single events. Fluctuating behaviour can be expected in real world use patterns (e.g. adjusting the hot water during a shower). The ability to track instantaneous ow rates was thus important and determined to be possible. The accuracy of ˙VE was not quantitatively assessed due to the large number
CHAPTER 6. RESULTS 90 of samples which would be required to be analysed as well as the uctuating nature of the estimated ow rate. The quantitative assessment of estimated ow rate accuracy was performed on the mean estimated ow rate, ¯˙VE.
6.4.2 Mean Flow Rate Estimation
It was shown in Section 6.2.1 that the estimated duration of ow events using vibration event detection is reliable. It was shown in Section 6.4.1 that the estimated instantaneous ow rate, ˙VE, is reliable above 5 L min−1. ¯˙VE is the normalised integral of ˙VE over the temporal boundaries of the event. If the temporal boundaries as well as ˙VE are accurate then ¯˙VE accuracy can be assessed.
It can be seen from gures 6.5 and 6.6 that although ˙VE closely follows ˙VM, the estimated ow rate uctuates. The mean ow rate per event, ¯˙V, is a consistent value to use as the uctuations are disregarded. Analysis of the measured and estimated mean ow rates per event, ¯˙VM and ¯˙VE respectively, was performed for Datasets 1, 2 and 3.
Figure 6.5 shows that the mean ow rates, ¯˙VM and ¯˙VE, are accurate for uctuating ow rates (15:00 to 15:02 scheduled event) and constant ow rates (15:05 to 15:07 and 15:10 to 15:15 scheduled events). Figure 6.6 contains a usage event between 16:20 and 16:23 which shows the same trends of accurate instantaneous and mean ow rate estimation. The ow event occurring between 16:20 and 16:23 in Figure 6.6 is the longest duration ow event which only contains ow rates greater than 5 L min−1. Flow events with shorter durations were observed to overestimate the mean ow rate. Many short duration ow events have prominent ˙VE spikes at the start and end of each event. Larger σ values were thus present at event edges, which means that vibrations from the manually controlled BV may have caused these spikes and contributed to ˙VE overestimation in Dataset 2. The peaks at event edges contribute less to longer duration events which corresponds to the observation that the longest duration ow event in Dataset 2 has the lowest estimation error for mean ow rate as can be seen in Table C.2.
Constant hot water ow rates are not expected in real world applications for the entire duration of a usage event. The presented data shows that the instantaneous ow rate can be used to calculate a mean value which appears to be accurate. Varying ow rates per usage event should be the most prone to average errors if the linear approximation is invalid but this is not the case - calculated mean ow rates for varying ow rates during events seems to be possible. This provides justi cation to focus on the measured and estimated mean ow rates per usage event and analyse the accuracy of the estimated mean ow rates.
Figure 6.7 shows the percentage ¯˙VE error of the system for mean ow rates per identi ed reliable usage event in the experimental unit. The histogram shows that the majority of usage events have a low estimation error. Dataset 2 consisted of short duration, manually controlled ow events, therefore the overestimation due to start and stop vibration peaks contributed to larger estimation errors. Datasets 1 and 2 contained automated ow event control only and do not contain outliers like Dataset 2. This indicates that the manually controlled BV caused larger vibrations which resulted in higher estimated ow rates when BV was adjusted, and thus larger ¯˙VE values.
−10 −5 0 5 10 15 20 25 30 0 2 4 6 8 10 ¯˙ VE Error [%] Frequenc y
Flow Rate Estimation Error per Reliable Usage Event Dataset 1 Dataset 2 Dataset 3
Figure 6.7: Flow rate estimation error per reliable usage event in Datasets 1, 2 and 3. The histogram shows the frequency and ow rate estimation error, ¯˙VE Error, as a
percentage of ¯˙VM. Only ow events which were marked as reliable by the algorithm
are shown. The histogram is cumulative.
0 2 4 6 8 10 12 14 16 18 20 22 100 101 102 103 ¯˙ VM [L min−1] Absolute ¯ ˙ VE Error [%]
Flow Rate Estimation Error for All Usage Events Dataset 1 Dataset 2 Dataset 3
Figure 6.8: Absolute usage event ow rate estimation error relating to measured ow rate. The minimum ow rate threshold for quantitative estimation, ¯˙V(min) of 5 L min−1, is indicated by a black dotted line.
CHAPTER 6. RESULTS 92 Figure 6.8 shows the absolute error of ¯˙VE as a percentage as a function of the measured ow rate. It can be seen that the system performs signi cantly better when used to estimate ow rates which are greater than 5 L min−1. Figure 6.8 represents the absolute estimation error for all experimental unit ow events. For usage events with measured ow rates greater than 5 L min−1 in Dataset 1 the estimation error was below 11 %. The relationship between estimation error and ¯˙VM does not appear to be inversely pro- portional. Low ow rate estimations are not reliable and the highest ow rates are not the signi cantly more accurately estimated than medium ow rates. The linear estima- tion method is successful and the estimation error decreases by an order of magnitude for measured ow rates above ¯˙V(min).