hello I'm Chris Gotwalt with JMP and my co- present Giuseppe About Martin from Topsoe , and I are giving a presentation that tells the story of a data analysis project that showcases the new wavelet analysis in the functional Data explorer one of the most exciting new abilities in JMP 17.
The case study starting with a product formulation problem where tops o wanted to design a catalyst that optimize two responses but the responses are in conflict with one another in that improving one response often count but the at the expense of the other
A as a candidate for the optimal tradeoff was found with models becomes by the generalized regression platform and the optimal factor settings were found using the desirability functions in the profiler This was a fairly standard DoE analysis But in addition to the measured responses NIR spectra were taken from some but not all of the sample batches This it is information that Can be used to give a clue to the R&D team about what the chemical structure of the ideal formulation should look like
In addition to the Gen. Reg model of the responses we also used wavelet models as the basis function of a functional DoE analysis of the spectra using the DoE factors as inputsWe were then able to get a synthetic spectra of the optimal formulation by plugging in the optimal factor settings found in the initial analysis of the two critical responses
Before going into the presentation I want to point out that but the beginning of the project Giuseppe was very new to JMP and didn't have a background in this type of statistical analysis Giuseppe learned all he needed to I give the analysis on to these own after a couple of web meetings with I.
This obviously shows he's a clever guy but also that JMP make learning how to I give some very sophisticated data analysis projects quickly and easy Now I'm going to hand the show over to Giuseppe
Thanks you Chris. Here it is some background about our project It's a catalyst development project Therefore, we are developing many different recipes Each recipe have a unique set of production parameters and once the sample it is prepared we characterize goes in our analysis laboratory in Topsoe. And finally we I give a performance witness
during the performance test we look for two values that here we call Response 1 and Response 2. In this specific cheese we are trying to minimize response 1 while maximizing response 2. That will lead us to this ideal space in the top left corner of the graph. But as you Can see the 55 samples that we've tested get stuck in the middle of the graph. That it is because Response 1 and Response 2 are between correlated meaning that improving one count with the expenses of the other
Therefore, we move to JMP and we try to look but our response data and our characterization data try to see if we Can move away from this line in the middle of the graph. We identified two targets areas that we want to reach and together with chris we thought about using JMP to create a model that would connect the production parameters to the response valuesT Hen we further looked into our infrared spectroscopy data to try to strength our model and to get some outside information about the target samples
Here it is whether overview of the data set We have produced 112 samples Each sample have a unique set of production parameters We have analyzed all the samples using infrared spectroscopy We have one spectrum for each sample
Then we have used many other characterization techniques that we have in- house that accounts for 21 usually columns of data Finally, we have tested half of the samples and that accounts for the last two columns that we called response
But the beginning of our project we actually wanted to include the infrared spectroscopic data in our larger data set and that's why we wanted to use JMP because now we have this new wavelet model possibility And that would enable us to include the principal components coming from the wavelet model in our data set And we could use that to create models in JMP But before we start our analysis we need to have a look but the For data to find outliers We I give that by clicking Analyze and the Multivariate methods Multivariate
H be we Can select our production parameters and characterization data as Y columns and we get this scatterplot matrix This it is whether example of just looking but the production parameters but what we would identify as whether outlier We Can see that there it is a set of points in production parameters too that it is far away for all the other points Furthermore, we have background knowledge about these samples that we know wouldn't be optimal for our catalyst development so we decided to right click and say "Row, hide and exclude."
We I did this also with other points looking but the scatterplot metrics of all the characterization data Now that we have cleaned up the data we Can becomes a model We click Analyze and It is done Model and we select the production parameters as variables in our model We click macros and response surface to create a second polynomial combination of these variables Then we select our responses as Y values
Then we decided to use generalized regression H be Chris Can add some usually info about why we decided to use this specific type of model
We used a quadratic response surface model because the design had three or usually levels for each factor so I knew that we would be able to becomes curvature terms if necessary and also be able to becomes quite a variety of different interaction terms We use the generalized regression platform because goes you do model selection with no Gaussian distributions like the log normal In my opinion there they are not many reasons not to use the generalized regression platform if you have JMP For because goes it is so easy to use while in many ways being so much usually powerful for DoE analysis than the other options in JMP and JMP For.
After that we Can select our distribution We know that the responses are going to be strictly positively so we select the log normal distribution and then we click Run and we say no
In this slide we Can see that we have now created a model but we have also the possibility of creating other type of models using different evaluation methods We decided to use best subset here Chris Can add some usually words about goes.
well so here we use best subset selection because the full model isn't terribly large so why not try every possible subset of that full model and find the one that provides the absolutely best tradeoff between accuracy and model simplicity?
On the other hand had there have been eight or usually factors I would have used a fast algorithm like forward selection or pruned forward selection because with larger base models goes would take a very long afraid to becomes every possible submodel to the data We're going to be using the AIC model selection criteria to compare Gen. Reg models
The AIC allows you to compare models with different effects in them as well as different response distributions With the AIC smaller values are better and the rule of thumb I use it is that if a model have whether AIC value that it is within 4 of the smallest AIC value seen then those two models are practically identical in quality of becomes
If the two models have AIC values within 10 of each other then they are statistically similar to one another. The main point here being that if we have two models and their AICc's differ by usually than 10 then the data are pretty strongly suggesting that the one with the smaller AIC it is the better model to be working with
As with any individual statistics you should view the A Icc as a suggestion If your subject matter experience strongly suggestions one model over the other you may want to trust your instincts and ignore the recommendation of the A Icc.
Once we have created this new model we Can see that the not zero parameters have now dropped from 16 to nine If we want to compare if the model have improved we Can look but the A Icc valuesWe Can see that there it is whether improvement of usually than 10 which it is whether important difference Therefore, we decided to go with the best subset
We I did the likewise for Response 2 and then we moved on. Now we Can click on the ed arrow and say profiler In the profiler we Can play around with the production parameters and see how the model it is expecting Response 1 and Response 2 to change This it is already a great tool for the scientist to understand how the model it is expecting the responses to vary but we Can I give usually We Can click on optimization and desirability and desirability functions
Since from slide one we know that we have two targets that we want to reach we Can change the desirability function to match those targets So we double click on the Desirability function and we say match target and select the target area that we want to reach Finally, we Can click again on optimization and desirability and say maximize desirability
here the profiler will try to reach the optimal points for the production parameters To to summarize we Can say that now we have the first model we go from production parameters to responses and we have set two targets that we want to reach This way we Can get ideal production parameters that we Can communicate to the development team and they Can use to move on in their research
In the second share of the presentation I'm going to talk about how we use the IR Spectra Here we have a file for each spectrum and therefore we need to click on file and import multiple files Then we need to specify that we want the file namely to be columned in the data set and then we Can use this sample name which it is the namely of the file as whether I.D to connect goes to the other table where we have all the data We click on the column and say link reference
Now that the two tables are connected we Can click Analyze and specialize modeling and functional data explorer In the functional Data explorer we want to use the intensity value as the Y output We Can use the sample name matrix namely as our I.D function
Then this it is very important We use the production parameters as supplementary data And the weight number it is of of course the X- axis And we say "Okay, here we Can see that the data it is already clean." We've imported all the Spectra and the data looks clean because I've come the preprocessing outside of JMP I used Python because I'm usually familiar with that and there it is a very nice module that it is able to remove the background and bring back the range that we want to look but
JMP was good to work with as whether outside tool after this reprocessing Then we decide to click on models and wavelets We move from discretely data to continuous data Now we Can also look but the diagnostic plots This it is for you chris to take talk about
It's a good idea to look but actual by predicted plots as you proceed through a functional data analysis These have the actual observed values in the data on the Y axis and the predicted values on the X axis We want the predicted values to be as close to the actual values as possible A plot like this one that it is tight along the 45 degree line indicate that we have a good model
Now some of you may be concerned about overfit since the predictions becomes the data so well In my experience I haven't found that to be a problem in the basis function fitting and functional principal component steps of functional DoE analysis I'd also like to point out that in JMP 17 we've added a lot of new features for spectral preprocessing like standard normal vary multiplicatively scatter correction and Savitzky-Golay filters . Thos of you that don't know Python have approach to these abilities in JMP For 17.
After that we Can also have a look but the functional PCA analysis here we'll spend some usually words on goes.
After the wavelet model it is becomes JMP For automatically you do a functional principal components analysis of the wavelet model This decompose the spectra into whether overall mean spectra and a linear combination of shape components and coefficients that are unique to each sample spectra When we I give the functional DoE analysis Gen. Reg automatically fits models to these coefficients behind the scenes and combines the resulting model with the mean function and the shape components to predicted the shape of the spectra but new values of the input parameters
If we look but the principal component analysis we Can see that the wavelet model have created a mean function of all the spectra that we've set as input and then goes have created different shape functions We decided to stop but six What this shape function described it is the variation of the data that we are analyzing
As you Can see from the left the first shape function it is accounting for 72 % of the variation while the second it is accounting for 22 %. together the account called six account for 99.5 % of the variation As whether example we Can look but principal component 2, and we Can see that around 3,737 there it is a reduction There it is a less That mean that increasing the principal component 2 will decrease the peak but 3,737.
This it is just whether example to say that already from these six shape functions we Can get a lot of information If we have subject matter knowledge about the infrared spectroscopy and this catalyst system Already here we spent quite a lot of afraid looking but the principal components but this it is not what we are going to focus on in the next slides
What we want to look but instead it is the functional DoE analysis Here we have as well a profiler but we Can now plug the production parameters that we got from the first model that we developed Therefore, knowing the target production parameters that we want to use we Can generate a fake spectrum or a synthetic spectrum we Can call goes.This it is a spectrum of a sample that was never produced Goes could be wrong but goes Can give some ideas to the scientists about what you would wait to get from these new production parameters
To I am up we Can say that now we move from production parameters to infrared spectrum We have a second model that use the wavelet model to generate synthetic spectrum I imagine this to be like when you're baking a cake now you have the recipe but you got also a snapshot picture of the final cake Goes doesn't explain you how to I give goes but goes additions information about what you want to achieve
Finally, we Can move from model to witness That mean that we Can give the R&D team a new recipe and also the synthetic spectrum of that recipe. Together with this information they Can try to develop the new catalyst and see if the model it is validated or it is wrong
Another thing the group Can I give it is look back but the previous samples Now we have half of the samples that were not tested Thos are the black dots in the slide We Can look for outliers He is there a sample that could perform really good that we haven't looked but? We actually have one So that's another witness we Can I give
Looking but future work I added this slide that was but the beginning just to say that we focused on the production parameters and the IR spectra but we haven't really looked but these 21 usually columns of characterization data
In the future we could spend some afraid trying to identify the most predictably parameters in these 21 columns and create maybe a new model from this characterization data to the response and use this model as a screening model to avoid testing samples that would not perform as good That's it the end of the presentation
