How strong is the correlation

Fred_Kohlhepp · ‎Oct 13, 2014

I have a system that has a number of thermocouples that is reporting a thermal strain. The strain appears to be dependent on the thermocouple readings, but not all of the thermocouples will affect the readings as much as some others.

Given a dataset, how can I rank the influence levels of the thermocouples?

StuartBruff · ‎Oct 13, 2014

Principal Component Analysis?

Stuart

AndyWesterman · ‎Oct 14, 2014

Plotting a 'points' type graph of the strain against the temperature for each (single) thermocouple should give a quick (and dirty) view of the relationship to each probe.

no effect / linear / polynomial / exponential ...

from that you should be able to minimise thenumber of probes to consider & the next steps will depend on what outcome(s) you need.

If the data is in an array / matrix then it should be possible to create the graph with an index to step through the probes one at a time to minimise the overhead of multiple graphs.

Regards

Andy

Fred_Kohlhepp · ‎Oct 14, 2014

A Westerman wrote:
Plotting a 'points' type graph of the strain against the temperature for each (single) thermocouple should give a quick (and dirty) view of the relationship to each probe.
no effect / linear / polynomial / exponential ...
from that you should be able to minimise thenumber of probes to consider & the next steps will depend on what outcome(s) you need.
If the data is in an array / matrix then it should be possible to create the graph with an index to step through the probes one at a time to minimise the overhead of multiple graphs.
Regards
Andy

Would that it were that simple!! The attached file has my data set; it's difficult to pick out which temperature measurement is most responsible for each measurement let alone decide on a function type.

AndyWesterman · ‎Oct 15, 2014

Hi Fred,

If I understand correctly, you have 32 thermocouples, 16 outputs and the data is 8 runs that have been added sequentially to the dataset.

Taking one condition (at "random" , honest).

output 1 and thermocouple 10:

Video Link : 5361

most of the runs show significant change in stress for no tc change , but run 6 seems to show a linear dependance & run 7 a step variation.

Now , I may not have seperated the runs correctly & this may lead to oddities. But given the inconsistency in this run , it might be adviseable to look at the data for each run independantly.

Andy

AndyWesterman · ‎Oct 15, 2014

Hi,

Made a few modifications to the sheet,

There is so much noise & backlash in the data that it will be diffifult to extract too much data,

towards the end of the run for output 10 there does seem to be a reasonable correlation showing - so it might be a start point.

quite a few of the probes seem to show no effect at all

Starting with these two it might reduce the complexity of the problem.

Andy

Fred_Kohlhepp · ‎Oct 15, 2014

I appreciate the effort, and you certainly have found a way to visualize a complex problem. But I can't discard or ignore data; I'm allowed to discredit it, but I can't find a reason to discredit any of this data--all measurements are "true."

When I look at the physical problem it appears to simplify. If you look at BAL, the measurement of forces, you will find 4 (columns 6, 7, 14, and 15) that don't appear to change much overall. These four were measurements on seperate devices that don't appear to be affected by temperatures. The other 12 measurements (0 thru 5 and 8 thru 13) are six-component strain-gaged transducers, and they have measurements that are drifting as the temperature changes. (If the "balances" are isothermal the readings are stable, repeatable and predictable.)

We can't keep them isothermal, when the machine runs it generates heat. We have installed heaters on the balances and are working at approximating isothermal, but it's a work in progress.

Each balance has four "flexures" that the strain gages are installed on. If the problem were simply thermal strain under the strain gages then measuring the temperatures of those flexures (the first eight columns of thermocouples) would deal with the problem. And, if I do a linear fit of gage outputs based on those eight TCs alone, I account for about 60% of the errors Adding the rest of the thermocouples raises that 60% to (maybe) 75%. That may just be due to adding that many more terms to the fit, and was part of the original question, "How can I rank the value of each thermocouple?" (Realize that I have 12 seperate problems.)

Fred

AndyWesterman · ‎Oct 16, 2014

Hi Fred,

First step to compare the results - is giving very inconclusive answers.

Its difficult, looking at the plots, to see any patterns (& the human advantage is to spot the general trends).

As stated before there are one or two TCs that show a consistent trend & it might be helpful to model these first.

The TCs that don't appear to correlate at all (either massive BAL swing for no TC change or vice versa) can be temporarily discounted & that may simplify the problem enough to see the next step.

At the moment , there are too many variables to work out the overall rules and the inconsistencies between runs make it almost certain that MathCad won't be able to calculate a result from the total dataset..

An alternate thought would be to take 1 set of data & work out the correlation for that.
Looking at the individual runs , there are still step functions that will not give rise to simple calculation.

There may be a case for editing the data to smooth some of the rough edges.

I know that long term you cannot discount any of the data , but we are lookiing for general trends at the moment & fine detail may never emerge due to the random 'error' content.

If possible then you can repeat the process for each the remainig data sets.

Each of the sets will almost certainly give different results, but you could then try to run statitistical analysis on the varying polynomial sets to give average values and (hopefully) standard deviations - might give some insight to the reliability of the averaged data.

Andy

Fred_Kohlhepp · ‎Oct 16, 2014

Thanks, Andy;

My problem is that I need to find the "magic bullet" that will collapse all these drifts to ± 4 counts (or so) and that's not achievable even within the data sets. (In order to get enough points to get a fit it may be necessary to merge data sets)

I can't find a physical model that points me at a curve to fit. I was hoping that there was a way to extract one from the data, and that smarter heads than mine might see it.