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- Curves that track along bounds of a data set

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Mar 2, 2017 12:56 PM
(1644 views)

8 REPLIES

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Mar 2, 2017 1:19 PM
(1596 views)

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.

Learn it once, use it forever!

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Mar 2, 2017 1:27 PM
(1592 views)

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!

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Mar 2, 2017 2:50 PM
(1577 views)

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!!

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Mar 3, 2017 6:12 AM
(1543 views)

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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Mar 3, 2017 8:15 AM
(1516 views)

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.

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Mar 3, 2017 12:41 PM
(1482 views)

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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Mar 2, 2017 1:22 PM
(1594 views)

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Mar 3, 2017 8:48 AM
(1509 views)