Friday, 11 February 2011

Identifying high confidence cycles

I now have two data sets that can be classed as possible cycles:
  • Each possible interval identified by thresholding
  • Every pair of 'on' and 'off' steady states
We know from the analysis of the fridge, the 'on' duration of each cycle has mean = 15 minutes and variance = 2 minutes. If we assume the duration of a cycle is normally distributed about the mean, we can create the following likelihood function:


Now we can filter out possible 'on' cycles below a likelihood threshold, leaving a set of cycles containing possible duplicates. We can remove duplicates by:
  • If two 'on' cycles overlap, discard the one with the lower likelihood
  • If two 'on' cycles are within the minimum 'off' duration of each other, discard the one with the lower likelihood
This produces a list of high confidence 'on' cycles. The next step is to identify any missing cycles between these, using a combination of:
  • Low confidence state-transitions
  • Possible intervals for fridge cycles
  • Applying the model of typical fridge behaviour using surrounding high confidence cycles

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