## Tuesday 8 February 2011

### Analysis and prediction of Alex's fridge's consumption

I've been analysing data collected from a meter connected to Alex's fridge to further investigate its consumption pattern. I've written an algorithm to detect the 'on' and 'off' transitions in the power data, and corrected these timestamps using the process described in my previous post. From this sequence of state transitions I have analysed the following 4 features:

On transition:
mean = 89W
variance = 13

Off transition:
mean = -83W
variance = 3

On duration:
mean = 15 minutes
variance = 2

Off duration:
mean = 35 minutes
variance = 38

Interestingly, the changes in power during transitions have a low variance, which is encouraging for classification purposes.

However, although the duration for which the fridge stays on also has a low variance, the duration for which it stays off has a high variance. Surprisingly, this suggests the fridge's temperature is regulated by varying the length of time between 'on' cycles. Should we want to predict the cycle of the fridge we need to model the pattern in the length of the 'off' periods. The graph below plots the duration of the 'off' cycle over a 4 day period.

Duration (minutes) of the fridge's 'off' cycle over a 4 day period

There is a clear pattern visible here which repeats every 24 hours (4 times on this graph). There is a steady increase overnight, peaking at around 6am. This is followed by a sharp trough most likely due to opening the fridge door at breakfast. The pattern over the remainder of the day is less predictable, although I would expect to see another trough around 7pm due to opening the fridge door when preparing dinner.

A suitable generalisation of this data would be useful to predict the time instants of 'on' and 'off' transitions in the fridge's cycle. This could be used to estimate the corresponding 'on' or 'off' transition should only one be extracted by steady-state analysis. In addition, it could be used to estimate both transitions in a cycle given either (or both of) the previous or following cycle's transitions.

In an attempt to model this data, I plotted a scatter of these day's data over the 24 hours and fitted a cubic function.

This would be of most use for long periods for which there have been no state transitions detected. A typical day has a period of roughly 17 hours where the fridge's signature might have not been detected at all. In this case, the curve would be used to estimate the off duration of each cycle, while keeping 'on' and 'off'power changes and the 'on' duration constant.