House temperature analysis
One of the things I've been curious about is how good house thermostats
are at keeping the temperature constant. I've lived in a number
of places where temperature varied over a wide range, but only recently
have I had a simple means of measuring temperature. This involved
the use of USB temperature monitors which are niftly little gadgets
which will store 11 days worth of temperature data sampling
once/minute. The USB temperature monitors are available from the
Weather Shop (link at WattsUpWithThat.com)
The temperature data which I recorded in the last two days was obtained
with one monitor next to my thermostat upstairs and a second monitor
2/3 of the way from floor to ceiling in basement as far away from
extraneous temperature sources as possible. The upstairs monitor
was an attempt to measure the temperature that the thermostat sees and
the downstairs monitor was in a portion of the house which is away from
windows and likely the most thermally stable area.
I tried this experiment once before but the data seemed
uninterpretable. It's because the temperature upstairs is kept
within rather narrow limits. Here is the graph of upstairs
All the above graph tells us is that the mean temperature upstairs is
72.27 F with a small SD. It also tells me that the thermostat is
way off in its calibration as that setting reads 68 F.
Much more information is available when one performs an FFT on the
data. The display below has an x-axis which is the reciprocal of
time so the units are hours/cycle rather than cycles/hour. I just
find hours/cycle a lot easier to wrap my head around instead of
constantly computing reciprocals of frequency in my head.
Note the prominent peak at about 2 hours/cycle. There are a lot
of other freqencies present there which I suspect are an artifact of
doing an FFT on square wave data. The point at 0 Hz has been
omitted (and has a value of 72.27 reflecting the mean of the
waveform). I suspect that the furnace has been coming on about
every 2 hours and to verify this now have another USB monitor hanging
right below one of the basement heat vents and, in 11 days assuming the
temperature outside doesn't change drastically, will have verification
or rejection of this hypothesis. The thermostat upstairs seems to
be working just as it was designed to do.
Most of my time has been spent in the basement as my computers live
there and I noticed that temperature appeared to fluctuate more
there. My temperature sense was proved correct when one looks at
the raw basement temperature data.
The basement is cooler by 0.76 F degrees on average and varies more
than the upstairs of the house. Still, the temperature is kept
within a 3 degree range. I suspect that the low temperatures on
9/10 February were due to sunny days which heated up the upstairs and
thus reduced the amount of time the furnace was on. Highest
basement temperatures are in the evening and this is likely due to
greater cooling of the upstairs during that time.
Where things get interesting is when one does an FFT of the basement
The basement temperature dominent frequency is 24.7 hours which I
suspect reflects the daily rhythm of external heating and cooling that
results in varying operation of the furnace. Not sure why it's
24.7 hours instead of 24. The 2 hour cycle is visible albeit
quite attenuated compared to the upstairs record.
This data analysis was just playing around with two of my toys; the USB
temperature monitors and DPlot program.
Looking at the upstairs data in the frequency domain provides way more
information than the raw temperature record. What would be really
need to put some of the cycles >24 hours into perspective would be
an outside temperature. I do have a third USB temperature monitor
but am currently unable to find a Canadian source of the 3.6 V Lithium
batteries that it needs (the greatest drawback of this other very neat
Data visualization is so much easier with DPlot than it was writing my
own VB programs to display data. DPlot can be scripted from VB
via DDE and that is the next project I plan on doing. Also, this
web page was a test of how easy it would be to organize my graphs of
various things I measure as HTML files.
Last modified 18/2/2011 T:=01:29