Viscosity evolution prediction (non linear platform)

[#1]

Hi all JMP user, 

I am trying to use several JMP tools to model and predict oil ageing as a function of temperature.

My model is calculated with the following equation:

η(t) model =η∞+(η0−η∞) e−kt with k=Aexp⁡(−EaRT)

In JMP, I defined η∞, A, and Ea as parameters (a, b, c), and I used the Nonlinear platform to estimate them by fitting the model to my viscosity measurements.

I have a few questions:

• I struggle to use the platform efficiently because I need to manually guess parameter values for a long time before the model converges to something reasonable.

• I noticed that the fitted parameters depend strongly on the initial values I provide. It seems that several different parameters can be found as long as you set up initially acceptable values. For me, that does not make sense. How should I handle this when I have no idea of the parameter values?

• I also tried using “Custom Inverse Prediction”, but I received an alert message. I guess that's means something is wrong with my model setup, so I should'nt trust my work :')

Any advice on how to properly set up and fit this type of Arrhenius‑based ageing model in JMP would be greatly appreciated. Thanks in advance 

[#2]

If I'm understand correctly, you might not need to use the Nonlinear platform, as Arrhenius transforms are built-in to many places in JMP. For example, the Fit Model platform can perform these transformations (and un-transform them automatically in the reports). 

The profiler takes this transformation into account, and shows temperature in un-transformed units:

 

[#3]

Hi Jed, 

Thanks for these tips. Honestly, I hadn't thought about using an Arrhenius transformation. 

However, I wanted to used a kinetic model to take into account the order of degradation reaction. I assume, the transformation is "order-agnostic". 

To clarify what I want to do is to extrapolate (time;temperature;viscosity) at lower temperature (40-60°C) and I must perform ageing at higher T because the viscosity is very stable over a very long period (several months, e ven years).

I used your fit to extrapolate the value at lower temperatures and the behaviour seems to be not coherent because below 80°C, the viscosity decreases over time and even reaches negatives viscosities (The viscosity is almost stable à 50°C for a very long period). 

In the profiler, at t0, the viscosity decreases when the temperature decreases

[#4]

Hi @PepinLB , 

The issues you describe are typical for many Nonlinear least-squares regression algorithms. Unlike linear regression, nonlinear regression fundamentally requires a "good guess" for the starting parameters, and there is no guarantee it will converge every time. JMP's approach to this is to use visualizations and "sliders" to allow you to easily set up the parameters before running the fit. You can also "lock" a parameter or set allowed ranges. 

Since you are doing a study of the "aging" of your product, that is, the change over time of its properties, I recommend using one of JMP's Degradation analysis platforms. Note that there are two platforms: "Repeated Measures Degradation" and "Degradation". If you will be doing this analysis often, I recommend reading those links to learn more about the advantages of each platform. Personally, I recommend starting with Degradation, especially since you are already familiar with the Nonlinear platform.

Using the Degradation platform, with a Nonlinear -> Constant Rate degradation path and a slight modification, I was able to get the attached result, which I think is similar to your desired equation. Does this look like a step in the right direction? 

- Christian 

[#5]

η∞: As t→∞, η(t) seems to fail to converge to a limit value.

Measurement errors may be relatively large.

The experimental design is somewhat inappropriate: typically, there are multiple samples (i.e., multiple traces) at each temperature.

Predicting response values in the range of 40-60°C via severe extrapolation is inappropriate.

If these issues are resolved, and you further master the Degradation Platform in JMP as well as the content of Statistical Methods for Reliability Data (Second Edition - William Q. Meeker), you will be fully capable of solving your problem.

[#6]

"Predicting response values in the range of 40-60°C is appropriate; the previous claim that this requires severe extrapolation and is inappropriate is incorrect."

[#7]

Hello Christian, 

Thank you very much for your precious advice. 

I used this plateform and try to start from the initial step. I managed to obtain an acceptable fit. However, I stil have a few comments ; 

1) How can I save the formula in a new column ? I don't manage to do that directly without copying and pasting the formula and editing the parameters value. Is there a way to save formula automatically like in another plateform ? Same question when using "Fit by System ID" ?

2) I used this plateform to fit data for a new product and exp. exp give the best fit but the increase is very sharp. I wanted to test "Custom" for path transformation to reduce the gap between experimental data and model. I was thinking about using power but I don't know how to try.

3) On your file, I could not enter any formula. I had to do in another data table

4) Coefficient analysis

Does it matter to review these coefficients when running this analysis ?

5) For some products, "repeated degradation" gives also a better (by chance when I play with parameters) but same issue, I don't find where to save the colomn formula. 

Thank you again for your help 

[#8]

I'm glad you were able to improve your fit. 

1) Unfortunately, I am not aware of any way to directly save the formula to a column the way you would do with other JMP platforms. This seems like it would be a good idea for our JMP Wish List. The way I save the formula is by copying the full formula text from the script window, and pasting it into the JMP Formula Editor in a new Formula Column. Then, I manually correct the Parameters to the fitted values from the Degradation report.

These steps can probably be scripted if it is a repetitive task, but for the first try it will need to be done manually. If any other JMP users know a better way, please comment here! 

I believe that when fitting by System ID, if each System ID was only tested at one temperature, the Arrhenius model will not be reliable (if it converges at all). 

2) For the new product, the degradation path does not appear to be steadily increasing. There is a "step" or "jump" at around 4000 H. This might be due to a real process or a measurement error. Either way, it does not appear that any smooth function such as a power law or exponential will fit well. You could filter the data to get it to fit, but then you risk having unreliable results. My suggestion would be to investigate that sample to determine the root cause of the unexpected "jump" at 4000H. 

That being said, to use a custom formula, you are always free to begin with an "Empty" formula window, and type in any formula and set of parameters you would like to use, just like in the Nonlinear platform. 

3) What version of JMP are you using? I created the table using JMP 19. 

4) Yes, it is important to consider the model report when running this analysis.

• AICc and BIC can be used to compare models.
• The T-test tells you whether the resulting parameter estimates are statistically significant.
• The Correlation is very important - a high correlation between model parameters can sometimes indicate that the model has more terms than necessary, and could be simplified. A high correlation also means there is a strong possibility that the parameter estimates are inaccurate, even if the model fits the data well. It is not uncommon in small datasets with a bit of measurement uncertainty, like this one.

Interpretation of nonlinear least-squares regression model fitting is a rich topic which is not just JMP-specific, so I would recommend finding some learning resources online. The JMP LearnBot may have some suggestions as well. 

5) I am also not able to find any way to export the model equation from the Repeated Measures Degradation platform, which seems a bit surprising. Again, maybe another user can comment here and let us know if there is a way to do this.