1. 10.02.06 1 WSC-5 Hard and soft modeling. A case study Alexey Pomerantsev Institute of Chemical Physics, Moscow

2. 10.02.06 2 WSC-5 Outlines 1.Background 2.Soft modeling 3.Hard modeling 4.Trade-off between hard and soft

3. 10.02.06 3 WSC-5 Part 1. Background

4. 10.02.06 4 WSC-5 Antioxidants Antioxidant is a special additive which inhibits polymers thermo- aging, protecting polymers from oxidation during processing as well as at the end-use application. The problem is to verify the quality (activity, effectiveness) of any new prospective chemical.

5. 10.02.06 5 WSC-5 Oxidation Induction Period - OIP T = 140°C t = 1- 90 days Conventional method is a Long Term Heat Aging (LTHA)

6. 10.02.06 6 WSC-5 Oxidation Initial Temperature - OIT Alternative method is Differential Scanning Calorimetry (DSC)

7. 10.02.06 7 WSC-5 Two Goals Soft/hard approaches trade-off 1$ Fast method for the antioxidants testing

8. 10.02.06 8 WSC-5 Sample Preparation 25 AO Samples Polypropylene (PP) 3 AO Concentrations 0.10 0.07 0.05

9. 10.02.06 9 WSC-5 DSC Experiments. Five Heating Rates

10. 10.02.06 10 WSC-5 Data

11. 10.02.06 11 WSC-5 Part 2. Soft Modeling

12. 10.02.06 12 WSC-5 Data Interpretation in Soft Modeling

13. 10.02.06 13 WSC-5 PLS1 Regressions: Xa i = y i X 3 models for each of initial AO concentration y 1 y 2 y 3

14. 10.02.06 14 WSC-5 PLS1 Regression. Three Data Sets A0A0 X expl Y exp RMSEC r 2 (cal) RMSEP r 2 (test) β 0.0599%92%0.290.960.240.990.8 0.0799%88%0.340.930.250.991.0 0.1099%84%0.400.910.340.971.2

15. 10.02.06 15 WSC-5 Prediction by PLS. Initial AO of 0.05

16. 10.02.06 16 WSC-5 SIC Principles All errors are limited! There exists Maximum Error Deviation, , such that for any error   Prob{|  | >  }= 0 RPV in parameter space RPV Prediction intervals: SIC & PLS

17. 10.02.06 17 WSC-5 SIC Prediction Intervals (PI). A 0 =0.05 Calibration Samples AO1-AO18 Test Samples AO19-AO25

18. 10.02.06 18 WSC-5 Part 3. Hard Modeling

19. 10.02.06 19 WSC-5 25 models for each of AOs Data Interpretation in Hard Modeling

20. 10.02.06 20 WSC-5 Two Steps of Hard Modeling How OIT ( T ) depends on heating rate ( v ), initial AO concentration ( A 0 ) T=T(v, A 0 ;  ) and parameter set  Step 1 How OIP (  ) depends on initial AO concentration ( A 0 )  =  (A 0 ;  ) and the same parameter set  Step 2

21. 10.02.06 21 WSC-5 Step 1. Model Building AO consumption AO critical value OIT model

22. 10.02.06 22 WSC-5 Fitter Calculations. Step 1

23. 10.02.06 23 WSC-5 Step 2. Model Building AO consumption AO critical value OIP modelOIP confidence bounds

24. 10.02.06 24 WSC-5 Fitter Calculations. Step 2

25. 10.02.06 25 WSC-5 Part 4. Trade-off between hard and soft

26. 10.02.06 26 WSC-5 OIP Prediction with Hard & Soft Methods A 0 =0.05

27. 10.02.06 27 WSC-5 Hard & Soft Statistics Cor (u soft, u hard ) Cor (y soft, y hard )

28. 10.02.06 28 WSC-5 PLS Score Plot. A 0 =0.05 CI < PI CI > PI

29. 10.02.06 29 WSC-5 Arrhenius Law

30. 10.02.06 30 WSC-5 ln(k c ) ^ Correlation Between the Estimates. A 0 =0.05 CI < PI CI > PI

31. 10.02.06 31 WSC-5 Forecast to the Different Conditions A 0 =0.04 & T=80ºC ÷ 200ºC

32. 10.02.06 32 WSC-5 SIC Object Status Plot (OSP) ?

33. 10.02.06 33 WSC-5 Pros and Cons Hard approachSoft approach Antioxidant type related modelsExperiment conditions related models Can forecast out of experimental area Cannot predict out of experimental area Has no strict limits of applicationHas strict rules of application The same average quality of prediction Different uncertainty for the different AOs Better for the worse AOsBetter for the better AOs Better to predict a given AO behaviorBetter to compare the different AOs

34. 10.02.06 34 WSC-5 Conclusions A long LTHA process (conventional approach) can be replaced with a fast DSC technique (novel approach) with further data calibration by the hard (NLR), or by the soft (SIC/PLS) methods. Both calibration methods have a similar quality of prediction. However, each technique has its own advantages and disadvantages.