1. Process – Structure Linkage for Cellulose NanoCyrstals (CNC)
Presentation – 3
Sezen Yucel

2. Process Parameters: Acid concentration & Process time
Dataset
Process Parameters: Acid concentration & Process time
58 %
62 %
64 %
60 mins
120 mins
105 mins
45 mins
75 mins
105 mins
C = 58, 62, 64 (%)
T = 45, 60, 75, 105, 120 (min)

3. Image Analysis Rods as ellipses Majoraxis ~ Length Minoraxis ~ Width
Histograms for length and width

4. Size Distributions (Length)
Probability Density Distributions

5. Size Distributions (width)
Probability Density Distributions

6. 1st Approach Probability 2nd Approach Probability & data
2 Approach for PCA
Example Data Set = {3, 5, 5, 6, 6, 6, 6, 7, 9,9}
Histogram of the Data
1st Approach
Probability
Same range for each data
0 for no-data 1 2 3 4 5 6 7 8 9 10
0.1
0.2
0.4
Frequency
Probability
2nd Approach
Probability & data 1 2 3 4 5 6 7 8 9 10
0.1
0.2
0.4
0.3
2.4
0.7
1.8
0.48
0.16
0.39
0.11
0.29
Weighted
Weighted/Sum

7. PCA results (1st approach – only probability
C = 64% T = 45, 75, 105 (min)
C = 62% T = 105 (min)
C = 58% T = 60, 120 (min)

8. PCA results (1st approach – only probability)
Basis Vectors for Length 1 2 3 4 5 6
PC1
-0.20
-0.24
-0.08
0.07
0.25
0.20
PC2
-0.04
-0.05
0.12
0.03
-0.01
PC3
0.06
0.004
0.001
-0.007

9. PCA results (2ND approach – probability & Data)
C = 64% T = 45, 75, 105 (min)
C = 62% T = 105 (min)
C = 58% T = 60, 120 (min)

10. PCA results (2ND approach – probability & Data)
Basis Vectors for Length 1 2 3 4 5 6
PC1
-0.19
-0.22
-0.08
0.05
0.26
0.19
PC2
-0.049
-0.06
0.135
0.028
-0.039
-0.016
PC3
-0.062
-0.059
-0.012
0.025
0.011
0.004

11. Desired model – Process structure linkage
(Acid Hydrolysis)
Structure
(Particle Morphology)
Concentration = 58, 62, 64 (%)
Time = 45, 60, 75, 105, 120 (min)
Inputs  Process Parameters Outputs  Size Distributions
L_d
W_d

12. First model - polynomial regression (1st order)
f1  R Square = .85 f2  R Square = .14 f3  R Square = .57
Fitting polynomial equations for PC scores
f1, f2, f3  MultiPolyRegress(X,Y,1)
Where X = Y =
PC1 = f1(C,T)
PC2 = f2(C,T)
PC3 = f3(C,T)
2nd order polynomial fitting  Overfitting C T 58 60
120 62
105 64 45 75
PC1
PC2
PC3
-0.20
-0.037
0.057
-0.237
-0.054
-0.05
0.083
0.115
-0.006
0.067
0.026
0.004
0.255
0.043
0.001
0.198
-0.007

13. A new model for small number of data such as:
Future work
A new model for small number of data such as:
Bayesian Linear Regression (BLR) Or
Gaussian Process Regression (GPR)
Hyperparameter optimization
Validation of the new model
(on the image which has different process parameters (C=62%, T=75 min) but less number of particles (~50)

14. Thank you & Questions