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Use of Functional Data Explorer in a Mixture Design for Tribological Performance Prediction (2021-EU-30MP-739)

Level: Intermediate


Victor GUILLER, R&D Engineer, FUCHS Lubrifiant FRANCE


Functional data creates challenges: it generates a lot of measurements, sometimes with redundant information and/or high autocorrelation, sampling frequency may not be regular, and it can be difficult to analyze the information or pattern behind the data. One very common practice is to summarize the information through some points of interest in the curves; maximum/minimum value, mean or other points are commonly chosen.

The study’s objective is to realize a mixture design for formulations containing up to three performance additives and analyze the results obtained from tribological equipment (friction coefficient vs. temperature). The first approach considered is to summarize the information through some values of interest: maximum friction coefficient and temperature at the maximum friction coefficient. This simple method enables us to find an optimal area for the formulation.

When using the Functional Data Explorer, tribological curves are modelled through a splines mathematical model. The connection between the mixture and the FDOE Profilers enables us to explore the experimental space and predict the tribological response of any formulation. This new approach enables a holistic view of the relevant systems behavior, allowing for increased understanding of more complex interactions typically neglected by conventional evaluation.

ERRATUM: At 05:30, the optimal mixture is composed of 70% of additive B and 30% of additive C (not additive A).
                   At 17:40, we evaluate the influence of additive B (not additive A).



Auto-generated transcript...




Victor GUILLER Hello everyone, so the topic of today is to use Functional Data Explorer in the mixture design in order to predict tribological performance.
  So the initial situation I will present you. So first the objective, we want to study and optimize the mixture of three performance additives
  with different chemistries in order to find the mixture with the highest performance, so that means the lowest and most stable friction coefficient versus the temperature,
  or the highest scuffing temperature. So the total amount of additive is fixed at 5% in oil in order to be able to spot differences between formulations
  and to avoid too big differences in viscosity between the additives in formulation. So here we will talk about tribology,
  which is the science and engineering of interacting surfaces in relative motions. It includes the study and application of the principles of friction, lubrication and wear.
  So as a mixture design, we will do a simplex centroid design. So as you can see here with so with additive A, B and C,
  we will use the dots here, the circle dots, for the...for doing the design of experiments is simplex centroid. And we will use the triangle points here
  as validation point for the model and, if necessary, these points can be used for augmenting the design and so doing an augmented simplex centroid design.
  In order to evaluate performances, we will use this tribometer here. It's a tribometer TE 77.
  We will measure the friction coefficient versus the temperature, so it starts from from 40 degrees to 200 degrees
  and with the contact points. So it's a ball on plate configuration under a certain normal load in an oscillating movement, as you can see on this figure. So the ball is isolated mechanically against the fixed lower plate and drive mechanisms run inside an oil bath.
  We have some challenges regarding this test, because for each testing, we have 4,140 data points that are recorded by the software in the system.
  So it creates particular challenges, because we generate a lot of measurements, so we may have some redundant information or high autocorrelation.
  And we may also have possible irregular sampling time or sampling frequency.
  And it can be quite difficult to analyze the information or pattern behind all of these points. So as an example, here is, as we can describe it, let's say a sea of data
  with all the experiments we have made for this design of experiments and all the friction coefficient curves versus the temperature.
  And the big question are, how can we use this data to predict something? So should we try to use only specific points from these curves or should we try to extract the relevant features from all the data, so from all the curves?
  So the first approach is a traditional approach that we will only use some specific points.
  If we look at friction coefficient curves versus temperature for the three additives alone here, we can spot some interesting points. For example,
  if we look at Additive C, so the friction curve in blue, we can spot here a peak, a scuffing peak, so we can record the temperature at the scuffing peak and the maximal friction coefficient
  recorded for this...for this peak. We can do the same for the additives so, for example, for Additive B, we have a higher scuffing temperature and also a
  lower friction coefficient here, and we can also see that for some experiments, for example here when we look at Additive A, we need to record several values. For example,
  we have here the first scuffing peak with a quite low friction coefficient, and then we have here, a second scuffing peak with a higher friction coefficient obtained. So we can use this information in the DOE
  in order to use the specific points in the model.
  So we will create a model with this specific points
  so that there are four responses and we are able to identify an area of interest
  in this mixture design. So we look here at the different responses, so we have quite a good modeling for all of these responses.
  And when we look at the end at the mixture profiler, we can see here an area of interest that is 70% of Additive B and 30% of Additive A. And in this area, we have the lowest friction coefficient and the highest
  scuffing temperature obtained.
  So what about the model accuracy and the predictive performances? So if we look at the differences between the experimental results and the prediction from the model and the augmented model,
  we can see that, for all of the experiments, we have a very little difference from...between experimental results and prediction from the model. So
  in this case, there is no use to include the validation point directly into the model because the simplex centroid design is able to to provide an
  accurate enough prediction for the friction...for the temperature at the first scuffing peak here.
  So as a conclusion, this first approach enables us to identify an optimal formulation area for performances, where we reach the highest scuffing temperature with the lowest friction coefficient,
  and the formulation in the center of this area is composed of 70% of Additive B and 30% of Additive C.
  When we do the same analysis approach with the Functional Data Explorer, we have a data table that looks like this, so we have here the ID corresponding to the
  DOE experiment number.
  Here, the proportion of Additive A, B and C and we record the temperature and we have the friction coefficient as a response here.
  But first, what is Functional Data Explorer? It's a platform designed for data are that are functions, signal or series, and it can be used as an exploratory data analysis, so this is our case here,
  or as a dimension-reduction technique.
  In this case, we will...we will use the Functional Data Explorer in order to create a model and be able to predict friction curves depending on the temperature.
  So, in order to do this we go on this data table on analyze, specialized modeling, Functional Data Explorer. We set the ID here as the ID function.
  Then we have the temperature as our input and the friction coefficient as our output.
  We have also information about the ratio of the additive, so we will save them in the supplementary variables, and we use the validation points from the mixture design, also as a validation here in our model.
  And we click on OK, but what we can see first is that we have a lot of variability here at the beginning of the tests.
  So first
  what we have to do is to remove all the point here with very low temperature, because you won't have scuffing peak,
  depending on the additives, but you have a lot of noise because it's initialization of the test. So in order to reach the first good temperature value, so around 40 degrees, you have to augment the temperature from room temperature to 40 degrees, and depending on the slope of this
  temperature variation, it can introduce some noise. So first, on
  the Functional Data Explorer, we will filter here on the temperature and we will only keep values that are above 45 degrees and then you can see, we will remove the noise at the beginning of the curves and we can set a model that will only explained variability depending on the additives.
  So, then, we create our P-Spline model. So first we have to select how much knots we will have in the model. So in this case when we use 158 knots, we have the best
  compromise in the modeling.
  Looking at the diagnostic plots, we can see that we have some variation and higher residuals when we have higher friction coefficient, which is quite normal because it's unstable situation.
  And the interesting part here is JMP is able to provide me the model for all of the curves. For each curves it's composed of mean curve here and some function here
  with coefficient linked to each of the function in order to express as accurate as possible all of the different friction curves.
  And we also have the nice part that because we have introduced the variables, so Additive A, B and C,
  we are able to change here the ratio of the additives in order to look.
  So I will do it also here.
  opening the P-Spline already.
  With 158 knots. Just to show you the interactivity between the rate...the additive ratio and the curve prediction from the model.
  So we have done our filtering before, and so at the end here, I can move...I can have here, for example, more Additive A or decrease the Additive B and see how it impacts
  my friction curve. The only problem of this profiler is that you don't have the constraint of the mixture design, so that means you can have more than 100% of the additive. So for example here, I can have 100% of Additive A but also Additive B and C.
  But still, it helps us to to know the interaction between the additives and the friction coefficient outcomes.
  If we are interested about the model accuracy and the predictive performances...sorry.
  Model accuracy and predictive performance, so we can have a look, for example here on this curve. So you have the experimental data points in blue and the smooth curve in red from the P-Spline model and, if we look also at
  what is our validation point, you can see that we have a pretty good match between experimental results and
  the prediction from the P-Spline model.
  So next what we want to do is to be able to screen through this experimental space from the mixture provider, but to have directly a link
  to show us what the friction coefficient curves look like, depending on how...where we are in this experimental space. So first we have to go into the DOE data table, so this one,
  and create an ID column here
  that will match the ID column of the Functional Data Explorer in the Functional Data Explorer data table. So here each experiments from the DOE is linked...has the same number as the ID column from the Functional Data Explorer table, so like this one.
  And then we have to, on the DOE table, we have to right click on ID and say link ID. And on the Functional Data Explorer table, we will do the same, link, but this time link reference, and we have to reference it to the previous data table, so from the DOE directly.
  When we have done this, we can open the Fit Group script from the DOE tables, so the one with the mixture profiler at the end here.
  And we will also open the Functional Data Explorer
  analysis from the Functional Data Explorer table.
  So the one i've already opened.
  So it just takes some seconds to open it.
  So I will put on the left
  the mixture profiler here, and on the right
  I will put the Functional Data Explorer analysis. And the last step we need to do is to link this two profilers, so I will go on the red triangle here, factor settings, and link profiler here.
  Just make sure that it's the same here.
  OK, so now when I've done this, so the two profiles are linked, so that means if I move here, I will just show you
  the curves here in the bigger screen, so if I move here my points, then I will have the prediction of the curves of the friction coefficient curves directly on the right.
  So it's's a very interactive tool in order to visually explore the area. And in our optimal area, you can see that the friction coefficient is quite stable and at the same value here.
  So here
  we can now use a mixer profiler to screen the experimental space and see how the predicted friction coefficient curves look like for any point of the experimental space.
  As a conclusion, so it's possible to determine and predict all friction coefficient curves in the experimental space and we have a better understanding of the influence additives. As an example here.
  So I'm starting from the middle here, if I move there, so that means i'm increasing the level of Additive A. You can see, on the right
  that we have a bigger slope here and highest scuffing peak
  when I'm moving closer to Additive A only.
  If i'm starting also from the middle and I increase the level of Additive C, you can see that the slope at the end of the profiler here decrease, but we have a very short scuffing peak here at around 80 degrees.
  Starting from the middle and going to Additive A, you can see that we still have
  a light slope here at the end, but no scuffing peak here. And when I'm in the area of interest here, I have the good aspects of the last two additives. That means
  I'm able to have no peak around 80 degrees and to have a stable friction coefficient also in this area.
  the mixture profiler and the functional design of experiment profiler.
  The advantages of the Functional Data Explorer approach...first, you analyze all the data points, so even if specific points can have similar value,
  the curve may behave differently. So here as an example, if you don't look at the friction coefficient value, you may say that you have very similar value because
  you have the same scuffing temperature for the two experiments, but, as you can see, you have very different friction coefficient obtained for the two experiments here.
  So second point is that you are able to do an objective analysis compared to a more subjective and domain-expert approach of selecting the right specific points and rule
  as a responses for the DOE. If we take here an example, we may ask ourselves what are the correct values for the DOE response? Should we consider this graphing peak or this one?
  Is this graphing peak too small or not to be considered? Should we consider this one? And is this graphing area also interesting
  for us on it? So it may be quite difficult in some situation to only spot specific value or specific point of interest. And, last but not least, as we have seen,
  it enables to have an interactive visualization and predictive modeling of the influence of additives on the formulation performances.
  So, as the benefits for FUCHS, as this new approach allows an increased understanding of the complex interaction between the additives that may be typically neglected by conventional evaluation and we have the possibility to build more precise predictive models.
  Thanks a lot for your attention.

Here is a reminder about the steps needed to create interactivity between Mixture profiler and Functional DoE profiler :

1- Create an ID column (character, nominal) on your DOE table that match the ID column (character, nominal) of the Functional datatable.

2- Right-click on ID column in DOE table and click on "Link ID".
3- Right-click on ID column in Functional datatable and click on "Link Reference" and choose the previous datatable (DOE table).

4- Open or create a "Fit Group" script from the DOE table and go to the Mixture profiler (to open it, click on the red triangle of "Fit group" and then select "Mixture profiler".
5- Open the Functional Data Explorer report from the Functional datatable and go to the FDOE profiler (to open it, click on the red triangle of "B-Spline"/"P-Spline" menu, and then select "Functional DOE Analysis").

6- Click on the red triangle of Mixture profiler (DOE datatable), then "Factor settings", and select "Link Profilers".

You can now use the mixture profiler to screen your experimental space, and see how the predicted curves look like for any point of your experimental space !

Thank you and very well done @Victor_G!  Your approach will be very useful throughout the chemical industry and beyond.


@Victor_G : very nice work! i am at the point in my FDE journey where i need to go backwards from FDE to process conditions/formulation. merci beaucoup!


@Bill_Worley : Thanks a lot Bill, I really like the work you have done on the pre-processing of spectral data, a lot of insights for daily work !
@markschahl : You're welcome, I'm glad if this presentation has helped you !
I will speak about this topic next week in the online meeting ENBIS, so in case you want to attend live or if you need more presentation supports, you can visit this page : ENBIS 2021 Spring Meeting (17-18 mai 2021): Use of Functional Data Explorer in a mixture design for ...