Aggregate & Truth Values

The graph below shows a plot of the household aggregate power demand (W) and sub-metered appliances over a 24-hour period. The household aggregate is shown in black, the fridge in blue, the washing machine in green and the dishwasher in red.

Calculating the individual appliance's demand from the household aggregate is equivalent to calculating the blue, green and red lines from the black line. To do this, at each possible position within the 24 hour period, the known signature of the appliance was subtracted from the aggregate, and the smoothness of the resulting data was calculated. This was repeated for each appliance in turn. Below are plots of the smoothness property at each position in the 24 hour period for the fridge, washing machine and dishwasher.

Fridge

Below is a plot of the smoothness function calculated for each possible subtraction of the fridge's signature from the aggregate plot. The y-axis is the smoothness measure, where a positive value represents a smoother plot after the signature was subtracted, while a negative value represents a less smooth plot.

We can see that this method works very well during the overnight period. However, during the day there are a number of false positives in addition to the correct detections. This is due to the fridge's relatively small power demand (90W) compared to the household average (500W).

Washing Machine

Below is a plot of the smoothness function calculated for each possible subtraction of the washing machine's signature from the aggregate plot.

This has worked well compared to the fridge. We can see one peak at around 300 on the x axis, which corresponds to a correct identification of the washing machine's cycle. However, there are also two false positives later in the day.

Dishwasher

Below is a plot of the smoothness function calculated for each possible subtraction of the dishwasher's signature from the aggregate plot.

The application of this technique to the dishwasher has been the most successful. We can see there are two clear peaks, both of which correspond to the two times the dishwasher was run in the 24 hour period. There are no false positives as with the other appliances, although the peaks do have some close matches of slightly lower values. The success of this method was due the dishwasher's unique signature; two cycles separated by a short interval.

Conclusions

This method works best for appliances:

- With large power demands compared to the average step change in the aggregate demand
- With signatures which describe a unique overall pattern

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