Next MBDoE Analyses

[bbefort]

Now that @jialuw96 was able to get Pyomo.DOE working and applied to the models in the R32/emimTF2N system, we can next do the following:

• [x] @jialuw96 will make a heatmap for the R32/emimTF2N system for the PR_quadTdep model
• [x] @dipperwang5 will do the information content analysis for the R32/emimTF2N system for the PR_quadTdep model
• [ ] @jialuw96, if time, will perform the FIM analysis for all the models for R125/emimTF2N and R32/bmimPF6 systems
• [x] @bbefort will send JW the data, parameters, and initial conditions for the other systems

Goal Timeline:

Friday, 10/21: -information content analysis complete @dipperwang5 -heatmap complete @jialuw96 -Model Selection slides sent to @adowling2 by @bbefort

Wednesday, 10/26: -FIM analysis complete for the other systems @jialuw96 @bbefort

Friday, 10/28: -full paper draft sent to everyone by @bbefort

[bbefort]

@jialuw96 I just updated the parameter values for:

R125/emimTF2N https://github.com/dowlinglab/extractive-distillation2/tree/mbdoe/modsel/paramest/emimtf2n/R125/Final_Results/MBDoE

Initial values: T = 283 - 323 K P = 100000 - 399800 Pa x = 0.1-0.55, 0.45 should be good

R32/bmimPF6 https://github.com/dowlinglab/extractive-distillation2/tree/mbdoe/modsel/paramest/bmimPF6/R32/Final_Results/MBDoE

Initial values: T = 283 - 323 K P = 399800 Pa x = 0.3-0.55, 0.45 should be good

[bbefort]

To Do Updates after 10/20 meeting:

@dipperwang5 To Do by Friday, 10/21:

• [x] Plot information content
• [x] Send information on the number and location of the X best experiments/data points (include all relevant details about data!)
• [x] Send AD, BB github notice when finished

@jialuw96 To Do by Friday, 10/21:

• [ ] Scale FIM calculations
• [ ] Save measurement values for each point (Pressure)
• [ ] Make a heatmap which includes MBDoE information and contours of pressure (measurements)

@bbefort To Do by Friday, 10/21:

• [x] Make a folder for KW information content and send to KW
• [x] Ask KB about pressure values
• [ ] Finish model selection slides and share with AD

[bbefort]

@dipperwang5 Ke, you can add your information content results in: https://github.com/dowlinglab/extractive-distillation2/tree/mbdoe/modsel/paramest/emimtf2n/R32/Final_Results/MBDoE/InfoContent

Please let me know if you have questions, thanks!

[dipperwang5]

@bbefort @adowling2

The kink occured in the six experiments:

The experiments with maximum D-optimality: (experiment count start with 0)

proposed experiment for 4 of experiment: (5, 8, 12, 26) proposed experiment for 5 of experiment: (4, 5, 12, 16, 25) proposed experiment for 6 of experiment: (2, 5, 12, 19, 23, 26) proposed experiment for 7 of experiment: (2, 5, 12, 16, 19, 23, 26) proposed experiment for 8 of experiment: (2, 3, 5, 12, 16, 19, 23, 26)

[adowling2]

Thank you. We'll ask you to rerun with new FIMs once Jialu changes the scaling.

For now, can you remake the plot by first dividing all of the FIMs by 1E-10 before calculating the determinant?

[adowling2]

@bbefort Once the FIM is rescaled, it will be sloppy until there are 6 experiments because there are 6 parameters. We should analyze the extra experiments (7th and 8th) and come up with a justification. Plotting the experiments in x vs T with dots and numbering them by order added may help.

[dipperwang5]

@adowling2 finished

[bbefort]

@adowling2 So the first six experiments are at 283K, then the 7th and 8th experiments start the next isotherm at 298K. Is this what you mean by justification? Once we add another temperature we get more information?

[adowling2]

Yes, but that does not make sense yet to me. My intuition is that the most informative experiments with be at the largest temperature or pressure differences.

[adowling2]

"proposed experiment for 6 of experiment: (2, 5, 12, 19, 23, 26)"

@bbefort How are the experiments numbered? Are these all at the same temperature or are you saying that experiments 0 to 5 are the same temperature? Happy to chat on Zoom tonight. I've got another call 8 - 9pm ET.

[adowling2]

@dipperwang5 Which branch contains your code?

[adowling2]

@bbefort Based on this file, here is my interpretation.

Best set of six experiments:	Row	T	P	xR32
2	283.15	399300	0.448
5	283.15	849400	0.786
12	298.15	999700	0.643
19	323.15	1000400	0.417
23	348.05	550300	0.175
26	348.05	1000500	0.288

These are spread out in temperature and composition, which makes sense to me. Here in the best 7th experiment:	Row	T	P	xR32
16	323.15	549500	0.264

And here is the best 8th experiment:	Row	T	P	xR32
3	283.15	549300	0.57

What do you think?

Edit: Can you make a plot in T vs xR32 space that uses 'o' for the first best 6, 'x' for the 7th, and 's' for the 8th. That will help us understand/interpret the results. You can then show all of the other experiments not included in this sets with a grey '.' with alpha=0.5 (50% transparency).

[dipperwang5]

@dipperwang5 Which branch contains your code?

mbdoe

[bbefort]

@adowling2 Best of six experiments:

Row	T	P	xR32
2	283.15	250300	0.306
5	283.15	700400	0.672
12	298.15	849500	0.57
19	323.15	700300	0.32
23	348.05	49700	0.084
26	348.05	850400	0.254

Yes to the general idea here, I think the numbers you showed are a bit off for some reason, but that's okay.

I will make the plot by tomorrow.

Talk to you soon. Thanks!

[adowling2]

@dipperwang5 I think there is a division or multiplication mistake. I expect rescaling will change log10 D-optimality from ~60 to ~1 or ~10. It increased the other way. Can you check the scaling?

[jialuw96]

@adowling2 @bbefort Here are heatmaps after scaling the pressure by 10^-5 (The prior information FIM is scaled by 10^-10):

The pressure is recorded and forms a heatmap:

Thank you!

[adowling2]

Can you exclude anything above 60 xR32 and post these plots? Those pressures are really high. Please also check the pressure units.

[jialuw96]

@adowling2 Yes, the pressure units are all in bar, it goes up for corner cases; For e.g., at the left bottom corner, the pressure is around: {"0": 0.60210417450390145, "1": 1.2341963962007638, "2": 1.9029835968426114}, while for the right upper corner, the pressure goes up to: {"123": 342.2220523455179, "124": 9505.802148693202, "125": 9363.331806334534}

I ploted the heatmap under x_R32 = 60%:

Pressure:

[adowling2]

@bbefort Do these pressures makes sense? How do they compare with the experiment data? These pressures seem high.

[adowling2]

@jialuw96 can you overlay all of the experimental data in the prior as black 'o' markers on the plots? That will help us interpret the results.

[adowling2]

@jialuw96 can you add a toggle that when plotting the FIM metrics you overwrite NaN if the pressure is above 10 bar (1 MPa)? My concern is that the contour plots show nothing interesting in the practical experimental region.

[jialuw96]

@adowling2 The heatmaps with experimental data overlapping:

There is a blank region in x = [0, 10%], this is because we start from 10%.

The NaN figures are:

Pressure:

[adowling2]

@jialuw96 Thank you, this is very informative.

Today (Friday), please do the following:

• [x] Extend the simulation window to ~1% xR32 (for a lower bound of 10%). Check this is feasible before trying it in a for loop. There might be initialization issues. Also, check what the smallest xR32 value in the dataset is. We want to cover that in the heatmap.
• [x] Fix the labeling issue. You have two A-optimality plots. I suspect one is actually D-optimality.
• [x] When you plot, overwrite all of the values above 20 bar with NaN.

Please work on this later next week (by today is great, but I can do an approximate job in PowerPoint if needed):

• [ ] After you plot the data, draw a polygon that covers the region with pressures greater than 15 bar. This should hide the "jagged" edges caused by the NaNs. To specify the polygon, you will need to compute the edges. This is easy for the top and right edges which are straight lines defined by the boundaries of the plot. For the curved portion of the polygon, you will need to use 2D interpolation to find xR32 coordinates as a function of T that results in 15 bar pressure. When you use the 2D interpolation function, the x, y, and z values may not be what you expect immediately.

After finalizing the formatting for the above requested plots:

• [x] We should also make one that shows the FIM metrics for the best set of 7 experiments and the best set of 8 experiments computed by @dipperwang5. Here we will use 'o' to mark the experiments chosen in the best set and '.' (with alpha=0.5 transparency) to mark the experiments not chosen. This will help us understand the smallest dataset requirements.

[bbefort]

@adowling2 The pressures Jialu shows at the temperatures and pressures for which we have data. I agree that the pressures become very high quickly beyond these regions and I think that's because the model will trend towards infinity. I think setting nan values about 20 bar should be reasonable per my conversation with Kalin. She said they are able to go a bit above 10 bar, but try not to exceed the HFC's vapor pressure, so 20 bar would push this a bit without being unreasonable.

[adowling2]

Let's also update the axes. "Temperature [K]" and "R-32 in Liquid [mol%]". @bbefort Please confirm if mol% or wt%.

[adowling2]

@bbefort I expect the heatmaps with all of the data to be fairly flat; adding another experiment nearby an existing experiment is not helpful. In contrast, I expect heatmaps made with only 6 experiments considered will be much more informative/interesting.

[bbefort]

@jialuw96 R-32 in Liquid [mol%]

[jialuw96]

@adowling2 @bbefort Heatmaps filling the blanks under 10% for x_R32, and increase the NaN bar to 20 bar:

[adowling2]

@dipperwang5 see comments on this thread

[dipperwang5]

Thank you. We'll ask you to rerun with new FIMs once Jialu changes the scaling.

For now, can you remake the plot by first dividing all of the FIMs by 1E-10 before calculating the determinant?

Hi Alex, I just want to double-check here. Dividing all of FIM by 1E-10 or 1E10?

[adowling2]

Divide by 1E10.