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Curves that track along bounds of a data set

dkraeuter_sunne

Community Trekker

Joined:

Jun 2, 2016

I have values recorded from a motor on a machine. I am trying to create curves that track along the top, middle and bottom of the data. Is there a way to do this in JMP or do I have to do it in a separate software. Attached are images of what I would like to do. Any feedback would be appreciated.

 

JMP Curves.jpg

8 REPLIES
markbailey

Staff

Joined:

Jun 23, 2011

I do not know if the curves are for visualization or if they need to be more precise, but you could compute a moving minimum and moving maximum (smoothing function) and then add them to your plot. The idea is similar to that of a moving average for for an extreme value instead. I don't know the best span for this purpose but you could make it variable and see what is the smallest span that gives you a good smooth. You might need to use a weighting scheme, too.

 

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markbailey

Staff

Joined:

Jun 23, 2011

Here is a simple demonstration formula using a short span = 3 but without weighting applied:

If( Row() > 1 & Row() < N Row( Empty() ),
	Maximum( :Oxy[Index( Row() - 1, Row() + 1 )] ),
	Empty()
)

You could use the Quantile() function instead of Maximum() to obtain other quantiles.

Learn it once, use it forever!
awallace

New Contributor

Joined:

Mar 2, 2017

I actually work with dkraeuter_sunne, and I would like to give a bit more of an explanation of our issue. The data that you are looking at is actually displaying a torque curve versus time. (I have attached some more pictures of our data.) As you may notice in the first picture, the top and bottom edges of the graphs "diverge" so to speak as time goes on in some of the runs. We need a way to capture the change in amplitude of these curves. 

 

This data is actually part of a large DOE. Therefore, we need polynomial fits that capture the "upper", "lower", and "mid" trends of the data. The coefficients would be then be used in our DOE as responses. Now, I have created a very complicated (and bulky) excel sheet to pull the upper and lower data points by essentially using numerical derivatives and change in sign of the slope, and it also pulls the 3rd order polynomial fit coefficients. The other two pictures show this. For this particular run, the excel sheet worked fairly well. However, this spreadsheet is far from being perfect as on other data sets there are some stray data points that get left behind which greatly skews the polynomial fits.   

 

Your suggestion of a moving maximum and moving minimum sounds like it might work well for us. My next question would be, do you know of a way to be able to export the polynomial coefficients? There will be 486 curves; so we need to automate it. 

 

Thanks!!

 

bivariate stroker.jpg

 

 

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bivariate.JPG

 

 

 

 

 

 

 

 

 

  

 

 

 

 

markbailey

Staff

Joined:

Jun 23, 2011

I wonder if quantile regresson might be a good method to model the median and the upper and lower extremes.

The noise is not constant over time, right? Also, is the noise a high frequence cycle or random? (Can't tell from the pictures.)

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dkraeuter_sunne

Community Trekker

Joined:

Jun 2, 2016

We will look into using the quantile regression to model the upper a lower extremes.

 

The "noise" isn't really noise but a change in the motor due to changing conditions in the process. While there is some noise, most of what you can see is just variation in the process.

markbailey

Staff

Joined:

Jun 23, 2011

Quantile Regression is a JMP Pro feature. Select Help > Books > Fitting Linear Models. See the chapter about Generalized Regression.

I think that there is a good chance that these models will simplify your data fitting process. The model is a single variable (time) and the sufficient order of the polynomial interpolating function won't be too high (quartic maybe).

Do not attempt to fit the extremes (0% or 100%) because there is little 'information' in your data about that location. Back off a bit (5% or 95%) and you should have enough information. The median (50%) is also available, of course.

This modeling is flexible and has fewer assumptions than linear regression. Plus, it provides a direct answer to your original question: the parameter estimates can be used as your experimental responses.

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Peter_Bartell

Joined:

Jun 5, 2014

One possible path through the Fit Y by X platform is to select the style model you want, polynomial, quadratic, etc. Then from the specific model fit hot spot in the report, select confidence curves individuals. You can adjust the alpha level to move the curves towards and away from the best fit line as you like to operationally define your criteria for your somewhat subjective idea of top, middle and bottom.

Peter_Bartell

Joined:

Jun 5, 2014

For still yet another idea...since this is time series data have you taken a look at the  Analyze -> Specialized Modeling -> Time Series Platform? All sorts of models can be built there, and most include the ability to save/plot prediction intervals with varying alpha levels.